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In the research and practice of multi-agent systems, formation path planning is particularly crucial, as it not only ensures the safe operation of agents but also enhances the efficiency of the system in task execution. This study introduces a multi-agent formation path planning method adapted for dynamic and complex environments, ensuring the system’s real-time responsiveness in dynamic obstacle avoidance and formation shape maintenance. This paper develops two core algorithms： One is dedicated to local motion planning and the other is focused on global path planning. The local motion planning algorithm iteratively uses semidefinite programming and quadratic programming to identify obstacle-free convex regions around agents and optimizes formation parameters through continuous convex optimization techniques. This approach effectively addresses the issue of multi-agent formation avoiding dynamic obstacles, ensuring the stability of the formation while adhering to environmental constraints. In the global path planning phase, this concept is further utilized by sampling obstacle-free convex regions in free space, combined with constraint optimization to calculate transitional formations between the initial and target formations, and employing graph search algorithms to find the optimal path to the target formation. This paper utilizes MATLAB to build a complex warehouse environment with both dynamic and static obstacles to verify the effectiveness of the method. It also compares the approach with the virtual structure method and probabilistic roadmap (PRM), demonstrating its superiority in terms of efficiency and accuracy. [ABSTRACT FROM AUTHOR]

Reservoir flood control scheduling is a challenging optimization task, particularly due to the complexity of various constraints. This paper proposes an innovative algorithm design approach to address this challenge. Combining the basic walrus optimization algorithm with the adaptive ε-constraint method and introducing the SPM chaotic mapping for population initialization, spiral search strategy, and local enhancement search strategy based on Cauchy mutation and reverse learning significantly enhances the algorithm's optimization performance. On this basis, innovate an adaptive approach ε A New Algorithm for Constraints and Multi Strategy Optimization Improvement (ε-IWOA). To validate the performance of the ε-IWOA algorithm, 24 constrained optimization test functions are used to test its optimization capabilities and effectiveness in solving constrained optimization problems. Experimental results demonstrate that the ε-IWOA algorithm exhibits excellent optimization ability and stable performance. Taking the Taolinkou Reservoir, Daheiting Reservoir, and Panjiakou Reservoir in the middle and lower reaches of the Luanhe River Basin as a case study, this paper applies the ε-IWOA algorithm to practical reservoir scheduling problems by constructing a three-reservoir flood control scheduling system with Luanxian as the control point. A comparative analysis is conducted with the ε-WOA, ε-DE and ε-PSO (particle swarm optimization) algorithms.The experimental results indicate that ε-IWOA algorithm performs the best in optimization, with the occupied flood control capacity of the three reservoirs reaching 89.32%, 90.02%, and 80.95%, respectively. The control points in Luan County can reduce the peak by 49%.This provides a practical and effective solution method for reservoir optimization scheduling models. This study offers new ideas and solutions for flood control optimization scheduling of reservoir groups, contributing to the optimization and development of reservoir scheduling work. [ABSTRACT FROM AUTHOR]

Background: CT reconstruction is of essential importance in medical imaging. In 2022, the American Association of Physicists in Medicine (AAPM) sponsored a Grand Challenge to investigate the challenging inverse problem of spectral CT reconstruction, with the aim of achieving the most accurate reconstruction results. The authors of this paper participated in the challenge and won as a runner‐up team. Purpose: This paper reports details of our PROSPECT algorithm (Prior‐based Restricted‐variable Optimization for SPEctral CT) and follow‐up studies regarding the algorithm's accuracy and enhancement of its convergence speed. Methods: We formulated the reconstruction task as an optimization problem. PROSPECT employed a one‐step backward iterative scheme to solve this optimization problem by allowing estimation of and correction for the difference between the actual polychromatic projection model and the monochromatic model used in the optimization problem. PROSPECT incorporated various forms of prior information derived by analyzing training data provided by the Grand Challenge to reduce the number of unknown variables. We investigated the impact of projection data precision on the resulting solution accuracy and improved convergence speed of the PROSPECT algorithm by incorporating a beam‐hardening correction (BHC) step in the iterative process. We also studied the algorithm's performance under noisy projection data. Results: Prior knowledge allowed a reduction of the number of unknown variables by 85.9%$85.9\%$. PROSPECT algorithm achieved the average root of mean square error (RMSE) of 3.3×10−6$3.3\,\times \,10^{-6}$ in the test data set provided by the Grand Challenge. Performing the reconstruction with the same algorithm but using double‐precision projection data reduced RMSE to 1.2×10−11$1.2\,\times \,10^{-11}$. Including the BHC step in the PROSPECT algorithm accelerated the iteration process with a 40% reduction in computation time. Conclusions: PROSPECT algorithm achieved a high degree of accuracy and computational efficiency. [ABSTRACT FROM AUTHOR]

BACKGROUND: The scientific revolution in the treatment of many illnesses has been significantly aided by stem cells. This paper presents an optimal control on a mathematical model of chemotherapy and stem cell therapy for cancer treatment. OBJECTIVE: To develop effective hybrid techniques that combine the optimal control theory (OCT) with the evolutionary algorithm and multi-objective swarm algorithm. The developed technique is aimed to reduce the number of cancerous cells while utilizing the minimum necessary chemotherapy medications and minimizing toxicity to protect patients' health. METHODS: Two hybrid techniques are proposed in this paper. Both techniques combined OCT with the evolutionary algorithm and multi-objective swarm algorithm which included MOEA/D, MOPSO, SPEA II and PESA II. This study evaluates the performance of two hybrid techniques in terms of reducing cancer cells and drug concentrations, as well as computational time consumption. RESULTS: In both techniques, MOEA/D emerges as the most effective algorithm due to its superior capability in minimizing tumour size and cancer drug concentration. CONCLUSION: This study highlights the importance of integrating OCT and evolutionary algorithms as a robust approach for optimizing cancer chemotherapy treatment. [ABSTRACT FROM AUTHOR]

This paper focuses on the cardinality constrained mean-variance portfolio optimization, in which only a small number of assets are invested. We first treat the covariance matrix of asset returns as a diagonal matrix with a special matrix processing technique. Using the dual theory, we formulate the lower bound problem of the original problem as a max-min optimization. For the inner minimization problem with the cardinality constraint, we obtain its analytical solution for the portfolio weights. Then, the lower bound problem turns out to be a simple concave optimization with respect to the Lagrangian multipliers. Thus, the interval split method and the supergradient method are developed to solve it. Based on the precise lower bound, the depth-first branch and bound method are designed to find the global optimal investment selection strategy. Compared with other lower bounds and the current popular mixed integer programming solvers, such as CPLEX and SCIP, the numerical experiments show that our method has a high searching efficiency. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by the National Natural Science Foundation of China [Grants 12101317, 12271071, and 11991024], the Natural Science Foundation of Jiangsu Province [Grant BK20200819], the Team Project of Innovation Leading Talent in Chongqing [Grant CQYC20210309536], the Contract System Project of Chongqing Talent Plan [Grant cstc2022ycjh-bgzxm0147], and the Philosophy and Social Science Fund of Education Department of Jiangsu Province [Grant 2020SJA0168]. K.F.C. Yiu is supported in part by the Research Grants Council of Hong Hong [Grant PolyU 15223419], the Hong Kong Polytechnic University [Grants 4-ZZPT and 1-WZ0E], and the Research Centre for Quantitative Finance [Grant 1-CE03]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0344) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0344). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems, in which the objective function is stochastic and the constraints are deterministic. The method proposed in this paper is a proximal gradient method that can also be applied to the composite optimization problem min |$f(x) + h(x)$|⁠ , where |$f$| is stochastic and |$h$| is convex (but not necessarily differentiable). Adaptive sampling methods employ a mechanism for gradually improving the quality of the gradient approximation so as to keep computational cost to a minimum. The mechanism commonly employed in unconstrained optimization is no longer reliable in the constrained or composite optimization settings, because it is based on pointwise decisions that cannot correctly predict the quality of the proximal gradient step. The method proposed in this paper measures the result of a complete step to determine if the gradient approximation is accurate enough; otherwise, a more accurate gradient is generated and a new step is computed. Convergence results are established both for strongly convex and general convex |$f$|⁠. Numerical experiments are presented to illustrate the practical behavior of the method. [ABSTRACT FROM AUTHOR]

This paper proposes a novel nature-inspired meta-heuristic algorithm, named Snow Geese Algorithm. It is inspired by the migratory behavior of snow geese and emulates the distinctive "Herringbone" and "Straight Line" shaped flight patterns observed during their migration. The algorithm is structured into three main phases for benchmark testing. In the first phase, the Snow Geese Algorithm's numerical results are compared with those of several classical meta-heuristic algorithms using the same test functions and original data from these algorithms. In the second phase, in order to minimize potential variations during the comparison, all algorithms undergo evaluation on a standardized testing platform. In the third phase, this paper applies the Snow Geese Algorithm to solve four widely recognized engineering optimization problems: the tubular column design, piston lever optimization design, reinforced concrete beam design and car side impact design. These real-world engineering problems serve as test cases to assess Snow Geese Algorithm problem-solving capabilities. The primary objective of the Snow Geese Algorithm is to provide an alternative perspective for tackling complex optimization problems. Please note that the complete source code for the Snow Geese Algorithm is publicly available at https://github.com/stones3421/SGA-project. • Snow Geese Algorithm: A novel meta-heuristic approach inspired by snow geese flight behavior, tackling optimization problems. • Two-stage Strategy: Mimics snow geese exploration and exploitation patterns, setting it apart from traditional methods. • Performance Evaluation: Multiple algorithms are assessed on different problems. • Algorithm Features: Experimental results validate the effectiveness of the Snow Geese Algorithm. • Practical Applications: Snow Geese Algorithm shows potential in engineering optimization, aiding accurate decision-making. [ABSTRACT FROM AUTHOR]

In this paper, a multi-fidelity Bayesian optimization approach is presented to tackle computationally expensive constrained multiobjective optimization problems (MOPs). The proposed approach consists of a three-stage optimization framework designed to search for promising candidate points. In the first stage, an acquisition function is proposed to identify a feasible solution if none is available in the current set of sampling points. Subsequently, a new multi-fidelity weighted expected hypervolume improvement function is developed to find better solutions. In the third stage, a constrained weighted lower confidence bound acquisition function is presented to enhance the constraint predictions and refine the solutions near the constraint boundary. Additionally, a filter strategy is suggested to determine whether constraint updating is necessary, aiming to save computational resources and improve optimization efficiency. Moreover, to expedite the optimization process, a parallel optimization approach is further developed based on the suggested three-stage optimization framework. To achieve this, a multi-fidelity influence function is introduced, allowing the proposed approach to determine a desired number of candidate points within a single iteration. Lastly, the proposed approach is demonstrated through six numerical benchmark examples, which verifies its significant advantages in addressing expensive constrained MOPs. Besides, the proposed approach is applied to the multiobjective optimization of a metamaterial vibration isolator, resulting in the attainment of satisfactory solutions. [ABSTRACT FROM AUTHOR]

Numerical simulations consist of many components that affect the simulation accuracy and the required computational resources. However, finding an optimal combination of components and their parameters under constraints can be a difficult, time-consuming and often manual process. Classical adaptivity does not fully solve the problem, as it comes with significant implementation cost and is difficult to expand to multi-dimensional parameter spaces. Also, many existing data-based optimization approaches treat the optimization problem as a black-box, thus requiring a large amount of data. We present a constrained, model-based Bayesian optimization approach that avoids black-box models by leveraging existing knowledge about the simulation components and properties of the simulation behavior. The main focus of this paper is on the stochastic modeling ansatz for simulation error and run time as optimization objective and constraint, respectively. To account for data covering multiple orders of magnitude, our approach operates on a logarithmic scale. The models use a priori knowledge of the simulation components such as convergence orders and run time estimates. Together with suitable priors for the model parameters, the model is able to make accurate predictions of the simulation behavior. Reliably modeling the simulation behavior yields a fast optimization procedure because it enables the optimizer to quickly indicate promising parameter values. We test our approach experimentally using the multi-scale muscle simulation framework OpenDiHu and show that we successfully optimize the time step widths in a time splitting approach in terms of minimizing the overall error under run time constraints. [ABSTRACT FROM AUTHOR]

In this paper, we consider finite sum composite optimization problems with many functional constraints. The objective function is expressed as a finite sum of two terms, one of which admits easy computation of (sub)gradients while the other is amenable to proximal evaluations. We assume a generalized bounded gradient condition on the objective which allows us to simultaneously tackle both smooth and nonsmooth problems. We also consider the cases of both with and without a quadratic functional growth property. Further, we assume that each constraint set is given as the level set of a convex but not necessarily a differentiable function. We reformulate the constrained finite sum problem into a stochastic optimization problem for which the stochastic subgradient projection method from Necoara and Singh [Stochastic subgradient projection methods for composite optimization with functional constraints; 2022 Journal of Machine Learning Research, 23, 1–35] specializes in a collection of mini-batch variants, with different mini-batch sizes for the objective function and functional constraints, respectively. More specifically, at each iteration, our algorithm takes a mini-batch stochastic proximal subgradient step aimed at minimizing the objective function and then a subsequent mini-batch subgradient projection step minimizing the feasibility violation. By specializing in different mini-batching strategies, we derive exact expressions for the stepsizes as a function of the mini-batch size and in some cases we also derive insightful stepsize-switching rules which describe when one should switch from a constant to a decreasing stepsize regime. We also prove sublinear convergence rates for the mini-batch subgradient projection algorithm which depend explicitly on the mini-batch sizes and on the properties of the objective function. Numerical results also show a better performance of our mini-batch scheme over its single-batch counterpart. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to test the performance of the recently proposed weighted superposition attraction-repulsion algorithms (WSA and WSAR) on unconstrained continuous optimization test problems and constrained optimization problems. WSAR is a successor of weighted superposition attraction algorithm (WSA). WSAR is established upon the superposition principle from physics and mimics attractive and repulsive movements of solution agents (vectors). Differently from the WSA, WSAR also considers repulsive movements with updated solution move equations. WSAR requires very few algorithm-specific parameters to be set and has good convergence and searching capability. Through extensive computational tests on many benchmark problems including CEC’2015 and CEC’2020 performance of the WSAR is compared against WSA and other metaheuristic algorithms. It is statistically shown that the WSAR algorithm is able to produce good and competitive results in comparison to its predecessor WSA and other metaheuristic algorithms. [ABSTRACT FROM AUTHOR]

Feature detection and matching is the key technique for remote sensing image processing and related applications. In this paper, a PDE-constrained optimization model is proposed to determine the scale levels advantageous for feature detection. A variance estimation technique is introduced to treat the observation optical images polluted by additive zero-mean Gaussian noise and determine the parameter of a nonlinear scale space governed by the partial differential equation. Additive Operator Splitting is applied to efficiently solve the PDE constraint, and an iterative algorithm is proposed to approximate the optimal subset of the original scale level set. The selected levels are distributed more uniformly in the total variation sense and helpful for generating more accurate and robust feature points. The experimental results show that the proposed method can achieve about a 30% improvement in the number of correct matches with only a small increase in time cost. [ABSTRACT FROM AUTHOR]

In this paper, rigid body static optimization is investigated on the Riemannian manifold of rigid body motion groups. This manifold, which is also a matrix manifold, provides a framework to formulate translational and rotational motions of the body, while considering any coupling between those motions, and uses members of the special orthogonal group SO (3) to represent the rotation. Hence, it is called the special Euclidean group SE (3) . Formalism of rigid body motion on SE (3) does not fall victim to singularity or non-uniqueness issues associated with attitude parameterization sets. Benefiting from Riemannian matrix manifolds and their metrics, a generic framework for unconstrained static optimization and a customizable framework for constrained static optimization are proposed that build a foundation for dynamic optimization of rigid body motions on SE (3) and its tangent bundle. The study of Riemannian manifolds from the perspective of rigid body motion introduced here provides an accurate tool for optimization of rigid body motions, avoiding any biases that could otherwise occur in rotational motion representation if attitude parameterization sets were used. [ABSTRACT FROM AUTHOR]

In this paper, an improved retractable body model (IRBM) is established, which has an advantage in simulating the flexion-and-extension motion of skier's legs during carved turning and straight gliding. The trajectory optimization problem for the nonlinear alpine skiing system is transformed into a multi-phase optimal control (MPOC) problem. Subsequently, a constrained multi-phase trajectory optimization model is developed based on the optimal control theory, where the optimization target is to minimize the total skiing time. The optimization model is discretized by using the Radau pseudospectral method (RPM), which transcribes the MPOC problem into a nonlinear programming (NLP) problem that is then solved by SNOPT solver. Through numerical simulations, the optimization results under different constraints are obtained using MATLAB. The variation characteristics of the variables and trajectories are analyzed, and four influencing factors related to the skiing time are investigated by comparative experiments. It turns out that the small turning radius can reduce the total skiing time, the flexion-and-extension motion of legs is beneficial to skier's performance, and the large inclination angle can shorten skier's turning time, while the control force has a slight effect on the skiing time. The effectiveness and feasibility of the proposed models and trajectory optimization strategies are validated by simulation and experiment results. [ABSTRACT FROM AUTHOR]

Image enhancement is a vital process that serves as a tool for improving the quality of a lot of real-life applications. Fractional calculus can be utilized in enhancing images using fractional order kernels, adding more controllability to the system, due to the flexible choice of the fractional order parameter, which adds extra degrees of freedom. The proposed system merges two fractional order kernels which helps in image enhancement techniques, and the contribution of this work is based on the study of how to optimize this process. The optimization of the two fractional kernels was done using the neural network optimization algorithm (NNA) to utilize the best order for the two kernels. In this paper, three fractional kernels are studied to highlight the performance of image enhancement using fractional kernels against different metrics. Furthermore, three different combinations of two kernels are combined and studied to enhance the metrics score by utilizing two different fractional orders for each kernel. Various optimization algorithms are used to obtain the optimum fractional order for both single and combined kernels. Using the constrained NNA, the evaluation metrics of the image enhancement show a 33% increase in measure of enhancement metric (EME), 21% increase in contrast, and 4% increase in average gradient compared to the best-achieved metrics by the literature while keeping the similarity metric above 0.75. [ABSTRACT FROM AUTHOR]

This paper presents improved single- and multi-objective algorithms based on the original moth flame optimizer (MFO) to tackle the dynamic economic emission dispatch (DEED) problem that affects power systems operations. The DEED problem is a multi-objective optimization problem that is strongly constrained, multi-dimensional, nonlinear, and non-convex. It comprises several optimization criteria, many of which are in direct opposition to one another; therefore, no one solution is optimal with regard to all of those criteria. Firstly, an enhanced flame generation strategy is incorporated into the MFO algorithm to improve performance. Then, the improved MFO is combined with the crowding distance mechanism and non-dominated sorting framework to enhance the convergence rate and the quality of the results. This helps improve the convergence pace. Firstly, the proposed multi-objective moth flame optimizer (MOMFO) algorithm is validated using 15 ZDT and UF benchmark multi-objective test functions. Then, the nonlinear DEED problem is also solved by determining the feasible optimal solution using the MOMFO algorithm. The implementation of the MOMFO on 10-unit systems and the IEEE 30-bus test system is being done to display the ability to solve a nonlinear, non-convex, and constrained DEED optimization problem. The DEED problem is solved using the MOMFO algorithm and other state-of-the-art algorithms, such as the non-dominated sorting genetic algorithm-II (NSGA-II), the multi-objective teaching–learning-based optimization (MOTLBO) algorithm, and multi-objective reptile search algorithm (MORSA). The selection of the control parameters of the MOMFO can be decided from the algorithm's findings on different IEEE bus systems. This study also introduces a new technique for incorporating loss predictions using artificial neural networks into the DEED model. During each phase of the dispatch time, the trained neural network can make only a single forecast of the transmission loss. The performance of MOMFO is compared with NSGA-II, MOTLBO, and MORSA, and the results obtained for both benchmarks and DEED proved the superiority of the proposed algorithm in solving the DEED of the power systems. [ABSTRACT FROM AUTHOR]

In the present paper, the expected-value (EV) reformulation of a class of stochastic vector variational inequalities (SVVI) is investigated. By using the regularized gap function, the EV reformulation of SVVI is transformed into a constrained optimization problem. Then a sample average approximation (SAA) method is proposed for solving the constrained optimization problem. Under suitable assumptions, the limiting behaviors of the optimal values and optimal solutions of the approximation problem are investigated. Finally, the rates of convergence in the different senses of optimal solutions for sample average approximation problem are discussed under the error bound condition. [ABSTRACT FROM AUTHOR]

This paper proposes a novel Difference-of-Convex (DC) decomposition for polynomials using a power-sum representation, achieved by solving a sparse linear system. We introduce the Boosted DCA with Exact Line Search ( BDCA e ) for addressing linearly constrained polynomial programs within the DC framework. Notably, we demonstrate that the exact line search equates to determining the roots of a univariate polynomial in an interval, with coefficients being computed explicitly based on the power-sum DC decompositions. The subsequential convergence of BDCA e to critical points is proven, and its convergence rate under the Kurdyka–Łojasiewicz property is established. To efficiently tackle the convex subproblems, we integrate the Fast Dual Proximal Gradient method by exploiting the separable block structure of the power-sum DC decompositions. We validate our approach through numerical experiments on the Mean–Variance–Skewness–Kurtosis portfolio optimization model and box-constrained polynomial optimization problems. Comparative analysis of BDCA e against DCA, BDCA with Armijo line search, UDCA, and UBDCA with projective DC decomposition, alongside standard nonlinear optimization solvers FMINCON and FILTERSD, substantiates the efficiency of our proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we propose a modified general inertial Mann algorithm and prove that it generates a sequence which converges weakly to a fixed point of a nonexpansive mapping in Hilbert spaces. Moreover, by using the viscosity method, we introduce a general inertial viscosity algorithm and prove that it generates a sequence which converges strongly to a common fixed point of a countable family of nonexpansive operators. We also derive schemes for solving constrained convex optimization, monotone inclusion, and nonsmooth convex optimization problems. Finally, we apply one of our proposed algorithms to solve image restoration problem. [ABSTRACT FROM AUTHOR]

In this two-part study, we develop a general theory of the so-called exact augmented Lagrangians for constrained optimization problems in Hilbert spaces. In contrast to traditional nonsmooth exact penalty functions, these augmented Lagrangians are continuously differentiable for smooth problems and do not suffer from the Maratos effect, which makes them especially appealing for applications in numerical optimization. Our aim is to present a detailed study of various theoretical properties of exact augmented Lagrangians and discuss several applications of these functions to constrained variational problems, problems with PDE constraints, and optimal control problems. The first paper is devoted to a theoretical analysis of an exact augmented Lagrangian for optimization problems in Hilbert spaces. We obtain several useful estimates of this augmented Lagrangian and its gradient, and present several types of sufficient conditions for KKT-points of a constrained problem corresponding to locally/globally optimal solutions to be local/global minimizers of the exact augmented Lagrangian. [ABSTRACT FROM AUTHOR]

In the context of the rapid development of the Internet of Vehicles, virtual reality, automatic driving and the industrial Internet, the terminal devices in the network show explosive growth. As a result, more and more information is generated from the edge of the network, which makes the data throughput increase dramatically in the mobile communication network. As the key technology of the fifth-generation mobile communication network, mobile edge caching technology which caches popular data to the edge server deployed at the edge of the network avoids the data transmission delay of the backhaul link and the occurrence of network congestion. With the growing scale of the network, distributing hot data from cloud servers to edge servers will generate huge energy consumption. To realize the green and sustainable development of the communication industry and reduce the energy consumption of distribution of data that needs to be cached in edge servers, we make the first attempt to propose and solve the problem of edge caching data distribution with minimum energy consumption (ECDDMEC) in this paper. First, we model and formulate the problem as a constrained optimization problem and then prove its NP-hardness. Subsequently, we design a greedy algorithm with computational complexity of O (n 2) to solve the problem approximately. Experimental results show that compared with the distribution strategy of each edge server directly requesting data from the cloud server, the strategy obtained by the algorithm can significantly reduce the energy consumption of data distribution. [ABSTRACT FROM AUTHOR]

Adaptive cruise control (ACC) enables efficient, safe, and intelligent vehicle control by autonomously adjusting speed and ensuring a safe following distance from the vehicle in front. This paper proposes a novel adaptive cruise system, namely the Safety-First Reinforcement Learning Adaptive Cruise Control (SFRL-ACC). This system aims to leverage the model-free nature and high real-time inference efficiency of Deep Reinforcement Learning (DRL) to overcome the challenges of modeling difficulties and lower computational efficiency faced by current optimization control-based ACC methods while simultaneously maintaining safety advantages and optimizing ride comfort. Firstly, we transform the ACC problem into a safe DRL formulation Constrained Markov Decision Process (CMDP) by carefully designing state, action, reward, and cost functions. Subsequently, we propose the Projected Constrained Policy Optimization (PCPO)-based ACC Algorithm SFRL-ACC, which is specifically tailored to solve the CMDP problem. PCPO incorporates safety constraints that further restrict the trust region formed by the Kullback–Leibler (KL) divergence, facilitating DRL policy updates that maximize performance while keeping safety costs within their limit bounds. Finally, we train an SFRL-ACC policy and compare its computation time, traffic efficiency, ride comfort, and safety with state-of-the-art MPC-based ACC control methods. The experimental results prove the superiority of the proposed method in the aforementioned performance aspects. [ABSTRACT FROM AUTHOR]

AbstractPV (photovoltaic) systems, also known as solar panel systems, play an essential role in the mitigation of greenhouse gas emissions and the promotion of renewable energy. Through the conversion of sunlight into usable energy, electricity is generated without emitting greenhouse gases and producing pollutants. Notwithstanding the evolutionary significance of PV systems, the occurrence of defects and anomalies in PV systems may result in diminished power output, consequently impeding the efficiency of the systems and potentially resulting in hazards in certain circumstances. Therefore, early detection of faults and anomalies in PV systems is imperative to guarantee the reliability, efficiency, and safety of the systems. In this paper, we develop a signal decomposition for the purpose of anomaly detection in PV systems. The proposed methodology is grounded on the concept of low-rank and sparse decomposition, with consideration given to the signs of the decomposed low-rank and sparse components, as well as the smooth variations within and between periods in the mean signals. Through the implementation of Monte Carlo simulations, we showcase the efficacy of our proposed methodology in identifying anomalies of varying durations and magnitudes in PV systems. A case study is employed to validate the proposed methodology in detecting anomalies in real PV systems. [ABSTRACT FROM AUTHOR]

Orthogonally decomposable (odeco) tensors is a special class of symmetric tensors. Previous works have focused on investigating its E-eigenpairs problem, and made some theoretical achievements concerning the number and the local optimality of E-eigenpairs. However, concerning local optimality of each eigenpair, the existing work only analyzed the third-order tensor case. In this paper, we further exploit this issue for any higher-order tensors by checking second-order necessary condition of the related constrained optimization model and deducing an equivalent matrix formula criterion for local optimality identification. Finally, a generalized conclusion for local optimality of eigenpairs for odeco tensors is provided, and some simulated experiments are conducted for validation. [ABSTRACT FROM AUTHOR]

Supply Chain (SC) Optimization is a key activity in today's industry with the goal of increasing operational efficiency, reducing costs, and improving customer satisfaction. Traditional optimization methods often struggle to effectively use resources while handling complex and dynamic Supply chain networks. This paper introduces a novel biomimetic metaheuristic algorithm called the Wombat Optimization Algorithm (WOA) for supply chain optimization. This algorithm replicates the natural behaviors observed in wombats living in the wild, particularly focusing on their foraging tactics and evasive maneuvers towards predators. The theory of WOA is described and then mathematically modeled in two phases: (i) exploration based on the simulation of wombat movements during foraging and trying to find food and (ii) exploitation based on simulating wombat movements when diving towards nearby tunnels to defend against its predators. The effectiveness of WOA in addressing optimization challenges is assessed by handling the CEC 2017 test suite across various problem dimensions, including 10, 30, 50, and 100. The findings of the optimization indicate that WOA demonstrates a strong ability to effectively manage exploration and exploitation, and maintains a balance between them throughout the search phase to deliver optimal solutions for optimization problems. A total of twelve well-known metaheuristic algorithms are called upon to test their performance against WOA in the optimization process. The outcomes of the simulations reveal that WOA outperforms the other algorithms, achieving superior results across most benchmark functions and securing the top ranking as the most efficient optimizer. Using a Wilcoxon rank sum test statistical analysis, it has been proven that WOA outperforms other algorithms significantly. WOA is put to the test with twenty-two constrained optimization problems from the CEC 2011 test suite and four engineering design problems to showcase its ability to solve real-world optimization problems. The results of the simulations demonstrate that WOA excels in real-world applications by delivering superior solutions and outperforming its competitors. [ABSTRACT FROM AUTHOR]

In this paper, the general framework for contact-constrained topology optimization of Strömberg and Klarbring (2010) is extended to robust topology optimization. In doing so, a linear elastic design domain is considered and the augmented Lagrangian approach is used to model the unilateral contact. For topology optimization, the design space is parametrized with the SIMP-approach and the Sigmund's filter is applied. Additionally, the robust framework considers uncertainties at the contact support such as deviations of the geometry of the contact surface and the friction coefficient. Both uncertainties are described by the first-order second-moment method which leads to minimal additional costs. In fact, only two additional linear equations must be solved to obtain the robust objective and its gradient with respect to the design variables. Having both the objective and the gradient, the design update is computed with the method of moving asymptotes. The robust framework is applied to 2D and 3D examples to prove its scalability for real-world applications. [ABSTRACT FROM AUTHOR]

Many practical problems can be classified as constrained multi-objective optimization problems. Although various methods have been proposed for solving constrained multi-objective optimization problems, there is still a lack of research considering the integration of multiple constraint handling techniques. Given this, this paper combines the objective and constraint separation method with the multi-operator method, proposing a population feasibility state guided autonomous constrained evolutionary optimization method. This method first defines the feasibility state of the population based on both feasibility and ε feasibility of the solutions. Subsequently, a reinforcement learning model is employed to construct a mapping model between the population state and reproduction operators. Finally, based on the real-time population state, the mapping model is utilized to recommend the promising reproduction operator for the next generation. This approach demonstrates significant performance improvement for ε constrained mechanisms in constrained multi-objective optimization algorithms, and shows considerable advantages in comparison with state-of-the-art constrained multi-objective optimization algorithms. [ABSTRACT FROM AUTHOR]

We introduce DiffOpt.jl, a Julia library to differentiate through the solution of optimization problems with respect to arbitrary parameters present in the objective and/or constraints. The library builds upon MathOptInterface, thus leveraging the rich ecosystem of solvers and composing well with modeling languages like JuMP. DiffOpt offers both forward and reverse differentiation modes, enabling multiple use cases from hyperparameter optimization to backpropagation and sensitivity analysis, bridging constrained optimization with end-to-end differentiable programming. DiffOpt is built on two known rules for differentiating quadratic programming and conic programming standard forms. However, thanks to its ability to differentiate through model transformations, the user is not limited to these forms and can differentiate with respect to the parameters of any model that can be reformulated into these standard forms. This notably includes programs mixing affine conic constraints and convex quadratic constraints or objective function. History: Accepted by Ted Ralphs, Area Editor for Software Tools. Funding: The work of A. Sharma on DiffOpt.jl was funded by the Google Summer of Code program through NumFocus. M. Besançon was partially supported through the Research Campus Modal funded by the German Federal Ministry of Education and Research [Grant 05M14ZAM, 05M20ZBM]. J. Dias Garcia was supported in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001. B. Legat was supported by a BAEF Postdoctoral Fellowship, the NSF [Grant OAC-1835443], and the ERC Adv. [Grant 885682]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0283), as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0283). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

For an unbalanced cooperative game, its grand coalition can be stabilized by some instruments, such as subsidization and penalization, that impose new cost terms to certain coalitions. In this paper, we study an alternative instrument, referred to as cost adjustment, that does not need to impose any new coalition-specific cost terms. Specifically, our approach is to adjust existing cost coefficients of the game under which (i) the game becomes balanced so that the grand coalition becomes stable, (ii) a desired way of cooperation is optimal for the grand coalition to adopt, and (iii) the total cost to be shared by the grand coalition is within a prescribed range. Focusing on a broad class of cooperative games, known as integer minimization games, we formulate the problem on how to optimize the cost adjustment as a constrained inverse optimization problem. We prove NP -hardness and derive easy-to-check feasibility conditions for the problem. Based on two linear programming reformulations, we develop two solution algorithms. One is a cutting-plane algorithm, which runs in polynomial time when the corresponding separation problem is polynomial time solvable. The other needs to explicitly derive all the inequalities of a linear program, which runs in polynomial time when the linear program contains only a polynomial number of inequalities. We apply our models and solution algorithms to two typical unbalanced games, including a weighted matching game and an uncapacitated facility location game, showing that their optimal cost adjustments can be obtained in polynomial time. History: Accepted by Area Editor Andrea Lodi for Design & Analysis of Algorithms—Discrete. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72022018 and 72091210]; the Research Grants Council of the Hong Kong SAR, China [Grant 16210020]; Hong Kong Polytechnic University [Grant P0032007]; and the Youth Innovation Promotion Association, Chinese Academy of Sciences [Grant 2021454]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.0268. [ABSTRACT FROM AUTHOR]

This paper is concerned with the inverse electromagnetic scattering problem for anisotropic media. We use the interior resonant modes to develop an inverse scattering scheme for imaging the scatterer. The whole procedure consists of three phases. First, we determine the interior Maxwell transmission eigenvalues of the scatterer from a family of far-field data by the mechanism of the linear sampling method. Next, we determine the corresponding transmission eigenfunctions by solving a constrained optimization problem. Finally, based on both global and local geometric properties of the transmission eigenfunctions, we design an imaging functional which can be used to determine the shape of the medium scatterer. We provide rigorous theoretical basis for our method. Numerical experiments verify the effectiveness, better accuracy and super-resolution results of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper introduces the Botox Optimization Algorithm (BOA), a novel metaheuristic inspired by the Botox operation mechanism. The algorithm is designed to address optimization problems, utilizing a human-based approach. Taking cues from Botox procedures, where defects are targeted and treated to enhance beauty, the BOA is formulated and mathematically modeled. Evaluation on the CEC 2017 test suite showcases the BOA's ability to balance exploration and exploitation, delivering competitive solutions. Comparative analysis against twelve well-known metaheuristic algorithms demonstrates the BOA's superior performance across various benchmark functions, with statistically significant advantages. Moreover, application to constrained optimization problems from the CEC 2011 test suite highlights the BOA's effectiveness in real-world optimization tasks. [ABSTRACT FROM AUTHOR]

The paper is devoted to the theoretical and numerical analysis of the two-step method, constructed as a modification of Polyak's heavy ball method with the inclusion of an additional momentum parameter. For the quadratic case, the convergence conditions are obtained with the use of the first Lyapunov method. For the non-quadratic case, sufficiently smooth strongly convex functions are obtained, and these conditions guarantee local convergence.An approach to finding optimal parameter values based on the solution of a constrained optimization problem is proposed. The effect of an additional parameter on the convergence rate is analyzed. With the use of an ordinary differential equation, equivalent to the method, the damping effect of this parameter on the oscillations, which is typical for the non-monotonic convergence of the heavy ball method, is demonstrated. In different numerical examples for non-quadratic convex and non-convex test functions and machine learning problems (regularized smoothed elastic net regression, logistic regression, and recurrent neural network training), the positive influence of an additional parameter value on the convergence process is demonstrated. [ABSTRACT FROM AUTHOR]

This paper presents the development of an optimization and modeling method for the objective functions of output power, efficiency and weight of an outer rotor permanent magnet brushless DC (BLDC) motor based on radial basis function (RBF) approximation technique. The proposed RBF‐based Pareto optimization method requires less knowledge about electric/magnetic formulas and can replace conventional optimizations based on these equations with higher accuracy. To apply the proposed optimization method, the initial design should be developed using such equations. Therefore, RBFs are used to model and predict engine behavior. To optimize the objective functions, we used a genetic algorithm optimization technique with nonlinear electric and magnetic constraints to find the Pareto front set. The design obtained by the proposed radial basis function Pareto optimization (RBFPO) method was finally verified by Ansoft Maxwell. The results of optimal design using the RBFPO method have higher output power and efficiency. Also, in addition to the advantage of a favorable accuracy, RBF‐based models are significantly faster than models available in simulation tools. [ABSTRACT FROM AUTHOR]

• Propose a topology optimization method for large deformation-induced frictionless contact structures. • Develop a novel nodal density interpolation for the node-to-segment contact model. • Develop the P-norm aggregated strain energy constraint for strength design. • Potentially applicable to the design of functionally demanding wearable devices and soft robots. This paper developed a strength constrained topology optimization method for hyperelastic structures with large deformation-induced frictionless contact. The Neo-Hookean hyperelastic constitutive equation is adopted as the material model that incorporates both material and geometric nonlinearity. The large deforming contact is described by the node-to-segment algorithm. The topology optimization model is developed under the SIMP framework. Given the SIMP-related fictitious domain, we develop a nodal variable-based interpolation scheme to build smooth correlation between the contact force and nodal density variables, thus enabling the smooth transition and variation of contact conditions. Moreover, to guarantee the structure strength, local strain energy constraints are formulated and aggregated by the P-norm function. The details of sensitivity analysis are explicitly explained. At last, several benchmark examples are conducted that validate the proposed method. [ABSTRACT FROM AUTHOR]

A new bio-inspired metaheuristic algorithm named the Pufferfish Optimization Algorithm (POA), that imitates the natural behavior of pufferfish in nature, is introduced in this paper. The fundamental inspiration of POA is adapted from the defense mechanism of pufferfish against predators. In this defense mechanism, by filling its elastic stomach with water, the pufferfish becomes a spherical ball with pointed spines, and as a result, the hungry predator escapes from this threat. The POA theory is stated and then mathematically modeled in two phases: (i) exploration based on the simulation of a predator's attack on a pufferfish and (ii) exploitation based on the simulation of a predator's escape from spiny spherical pufferfish. The performance of POA is evaluated in handling the CEC 2017 test suite for problem dimensions equal to 10, 30, 50, and 100. The optimization results show that POA has achieved an effective solution with the appropriate ability in exploration, exploitation, and the balance between them during the search process. The quality of POA in the optimization process is compared with the performance of twelve well-known metaheuristic algorithms. The simulation results show that POA provides superior performance by achieving better results in most of the benchmark functions in order to solve the CEC 2017 test suite compared to competitor algorithms. Also, the effectiveness of POA to handle optimization tasks in real-world applications is evaluated on twenty-two constrained optimization problems from the CEC 2011 test suite and four engineering design problems. Simulation results show that POA provides effective performance in handling real-world applications by achieving better solutions compared to competitor algorithms. [ABSTRACT FROM AUTHOR]

Based on a coupling conjugation scheme and the perturbational approach, we build Fenchel–Lagrange dual problem of a composed optimization model with infinite constraints in separated locally convex spaces. This paper has mainly two targets. One is to establish strong duality under a new regularity condition (RCA) and an extension closed-type condition (ECRCA). The e-convex counterpart of Fenchel–Moreau theorem plays a key role in analysing the relation between them. The other aim is to achieve the sufficient and necessary characterizations for total duality in terms of c-subdifferentials. For this purpose, a formula for ε-c-subdifferentials of a proper function composed with a linear continuous operator is proved and applied. [ABSTRACT FROM AUTHOR]

One of the major challenges in finite element methods is the mitigation of spurious oscillations near sharp layers and discontinuities known as the Gibbs phenomenon. In this paper, we propose a set of functionals to identify spurious oscillations in best approximation problems in finite element spaces. Subsequently, we adopt these functionals in the formulation of constraints in an effort to eliminate the Gibbs phenomenon. By enforcing these constraints in best approximation problems, we can entirely eliminate over- and undershoot in one-dimensional continuous approximations, and significantly suppress them in one- and higher-dimensional discontinuous approximations. [ABSTRACT FROM AUTHOR]

This paper establishes a simplified model of a flexible beam with multiple nonlinear supports that present cubic stiffness to study the potential application of cubic nonlinearities in the vibration control of beams. The Lagrangian method (LM) is used to predict transverse dynamic responses of the flexible beam with multiple nonlinear supports that present cubic stiffness, whereas the harmonic balance method (HBM) and Galerkin truncation method (GTM) are utilized to study the accuracy of the LM. Against the background, the effect of nonlinear supports that present cubic stiffness on the nonlinear transverse dynamic responses of the beam is studied. For this study, the accuracy of the LM is guaranteed under the 4-term truncation number. Nonlinear transverse dynamic responses of the flexibly constrained beam with multiple nonlinear supports that present cubic stiffness are sensitively influenced by their initial calculation values. For different boundary conditions or working statuses, the maximum restoring forces at both ends of the flexible beam can be suppressed effectively by optimizing the parameters of nonlinear supports that present cubic stiffness. Appropriate parameters of nonlinear supports that present cubic stiffness are good at vibration control of the flexibly constrained beam. In addition, complicated dynamic responses of the flexible beam with multiple nonlinear supports that present cubic stiffness are motivated under some inappropriate parameters of nonlinear supports. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid algorithm called rough sine cosine algorithm (RSCA) is introduced for solving engineering optimization problems by merging the sine cosine algorithm (SCA) with the rough set theory concepts (RST). RSCA combines the benefits of SCA and RST to focus the search for a promising region where the global solution can be found. Due to imprecise information on the optimization problems, efficient algorithms roughly identify the optimal solution for this type of uncertain data. The fundamental motive for adding the RST is to deal with the imprecision and roughness of the available information regarding the global optimal, especially for large dimensional problems. The cut concept of RST targeted the more interesting search region so the optimal operation could be sped up, and the global optimum could be reached at a low computational cost. The proposed RSCA algorithm is tested on 23 benchmark functions and 3 design problems. RSCA's obtained results are mainly compared to the SCA, which is used as a first level of the proposed algorithm in this work and those of other algorithms in the literature. According to the comparisons, the RSCA can provide very competitive performance with different algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a delayed distributed proportional control is developed for a class of multiple-input-multiple-output systems in order to reduce the effects of external disturbances and uncertain dynamics. The system under consideration is a three degrees-of-freedom planar robot, consisting of an active joint driving the first link and passive flexible joints for the second and third links. The control challenge for this system is to drive the flexible arm around the desired setpoint or trajectory by controlling the first link. Actually, by using a specific Lyapunov-Krasovskii storage functional associated with a constrained optimization problem, the robustness of the proposed proportional retarded control action is achieved. This analysis, together with the attractive ellipsoid concept allows to conclude with Ultimately-Uniformly-Bounded stability. The closed-loop control algorithm is tested in numerical simulation and a comparative study with some existing recent control schemes based on the performance error is presented. • The proposed control scheme belongs to a class of multivariable proportional time delay distributed controller. • After finite time the trajectories of a flexible manipulator stay within reduced size attractive ellipsoid. • Ultimate Uniformly Bounded Stability of the controlled system is demonstrated by using a Lyapunov-Krasovskii functional. • The proposed algorithm can also be adapted for a class of nonlinear uncertain/disturbed multivariable output systems. • A sufficient condition to guarantee the feasibility of specific Bilinear Matrix Inequality is presented. [ABSTRACT FROM AUTHOR]

In this paper, we propose an improved enhancement space-variant anisotropic PDE-constrained for image denoising, based on a learning optimization procedure. Since the tensor structure of the Weickert-type operators encodes three critical parameters: λ 1 , λ 2 and θ , which define the local direction geometry in the image and also controls smoothing intensity along image features. We have then adopted an automatic estimation of these parameters based on a PDE-constrained optimization with a learning step of the additional information about the clean image. For the numerical solution of the computed free-noise image, we introduce a non-smooth Alternating Direction Method of Multipliers (ADMM) algorithm. The numerous tests in the experiments part incense, visually and quantitatively, the incomes of this new spatial tensor for PDE smoothing over the other denoising approaches. • An improved enhancement space-variant anisotropic PDE-constrained for image denoising is introduced. • An automatic estimation of the diffusion-tensor parameters based on a bilevel optimization with a learning step is involved. • A non-smooth ADMM algorithm is also performed to compute the solution of the optimization-constrained problem. • The comparative results demonstrate the performance of the proposed algorithm against complex noise structures. [ABSTRACT FROM AUTHOR]

The intermittent nature of wind power generation induces great challenges for power bidding in the electricity market. The deployment of battery energy storage can improve flexibility for power bidding. This paper investigates an optimal power bidding strategy for a wind–storage hybrid power plant in the day-ahead electricity market. To handle the challenges of the uncertainties of wind power generation and electricity prices, the optimal bidding problem is formulated as a risk-aware scenario-based stochastic programming, in which a number of scenarios are generated using a copula-based approach to represent the uncertainties. These scenarios consider the temporal correlation of wind power generation and electricity prices between consecutive time intervals. In the stochastic programming, a more practical but nonlinear battery operation cost function is considered, which leads to a nonlinear constrained optimization problem. To solve the nonlinear constrained optimization problem, an ensemble differential evolution (EDE) algorithm is proposed, which makes use of the merits of an ensemble of mutant operators to generate mutant vectors. Moreover, a problem-specific constraint-handling technique is developed. To validate the effectiveness of the proposed EDE algorithm, it is compared with state-of-the-art DE-based algorithms for constrained optimization problems, including a constrained composite DE (C2oDE) algorithm and a novel DE (NDE) algorithm. The experimental results demonstrate that the EDE algorithm is much more reliable and much faster in finding a better bidding strategy against benchmarking algorithms. More precisely, the average values of the success rate are 0.893, 0.667, and 0.96 for C2oDE, NDE, and EDE, respectively. Compared to C2oDE and NDE, the average value of the mean number of function evaluations to succeed with EDE is reduced by 76% and 59%, respectively. [ABSTRACT FROM AUTHOR]

The frequency- and temperature-dependent characteristics of viscoelastic materials significantly affect the vibration response of the damped composite structures. In this paper, an efficient strategy of hybrid expansion combined with dynamic reduction is developed to solve the steady-state response of the frequency- and temperature-dependent viscoelastic structure characterized by nonproportional system, and the sensitivity analysis is carried out based on the adjoint variable method. The similarity index is defined to distinguish the correlation among different design layouts. Two instances demonstrated the validity of the proposed approach. The findings indicated that a positive compromise between accuracy and efficiency can be achieved, and the computational time can be significantly reduced while ensuring the accuracy of the results. Furthermore, it has been discovered that the excitation frequency and temperature significantly impact the optimal configuration of damping material. The effects of layer thicknesses and volume fractions on optimization designs are also further investigated. [ABSTRACT FROM AUTHOR]

This paper uses an augmented Lagrangian method based on an inexact exponential penalty function to solve constrained multiobjective optimization problems. Two algorithms have been proposed in this study. The first algorithm uses a projected gradient, while the second uses the steepest descent method. By these algorithms, we have been able to generate a set of nondominated points that approximate the Pareto optimal solutions of the initial problem. Some proofs of theoretical convergence are also proposed for two different criteria for the set of generated stationary Pareto points. In addition, we compared our method with the NSGA-II and augmented the Lagrangian cone method on some test problems from the literature. A numerical analysis of the obtained solutions indicates that our method is competitive with regard to the test problems used for the comparison. [ABSTRACT FROM AUTHOR]

Probabilistic Latent Semantic Analysis (PLSA) is a fundamental text analysis technique that models each word in a document as a sample from a mixture of topics. PLSA is the precursor of probabilistic topic models including Latent Dirichlet Allocation (LDA). PLSA, LDA and their numerous extensions have been successfully applied to many text mining and retrieval tasks. One important extension of LDA is supervised LDA (sLDA), which distinguishes itself from most topic models in that it is supervised. However, to the best of our knowledge, no prior work extends PLSA in a similar manner sLDA extends LDA by jointly modeling the contents and the responses of documents. In this paper, we propose supervised PLSA (sPLSA) which can efficiently infer latent topics and their factorized response values from the contents and the responses of documents. The major challenge lies in estimating a document's topic distribution which is a constrained probability that is dictated by both the content and the response of the document. To tackle this challenge, we introduce an auxiliary variable to transform the constrained optimization problem to an unconstrained optimization problem. This allows us to derive an efficient Expectation and Maximization (EM) algorithm for parameter estimation. Compared to sLDA, sPLSA converges much faster and requires less hyperparameter tuning, while performing similarly on topic modeling and better in response factorization. This makes sPLSA an appealing choice for latent response analysis such as ranking latent topics by their factorized response values. We apply the proposed sPLSA model to analyze the controversy of bills from the United States Congress. We demonstrate the effectiveness of our model by identifying contentious legislative issues. [ABSTRACT FROM AUTHOR]

In a recent paper an Inexact Restoration method for solving continuous constrained optimization problems was analyzed from the point of view of worst-case functional complexity and convergence. On the other hand, the Inexact Restoration methodology was employed, in a different research, to handle minimization problems with inexact evaluation and simple constraints. These two methodologies are combined in the present report, for constrained minimization problems in which both the objective function and the constraints, as well as their derivatives, are subject to evaluation errors. Together with a complete description of the method, complexity and convergence results will be proved. [ABSTRACT FROM AUTHOR]

This paper presents a new optimisation method for PID controller cascaded with a lead-lag compensator (PIDC). Parameters of the controller are obtained by solving the constrained optimisation problem. We propose two variants of the optimality criterion. The first one is defined through the max–min optimisation problem wherein objective function is the amplitude frequency response of the PIDC controller. The second one is based on an effective approximation of the minimum value of the amplitude frequency response of the PIDC controller. Consequently, we obtain a computationally less expensive problem. Both variants of optimality criterion result in efficient load disturbance and noise rejection, while robustness is ensured by constraining the value of the maximum sensitivity Ms. Good reference shaping is supported with proper constraints based on the Amplitude Optimum (AO) principle. Numerous batches of processes typically encountered in the industry are used to demonstrate the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

This paper proposes a path-based approach for the minimization of a continuously differentiable function over sparse symmetric sets, which is a hard problem that exhibits a restrictiveness-hierarchy of necessary optimality conditions. To achieve the more restrictive conditions in the hierarchy, state-of-the-art algorithms require a support optimization oracle that must exactly solve the problem in smaller dimensions. The path-based approach developed in this study produces a path-based optimality condition, which is placed well in the restrictiveness-hierarchy, and a method to achieve it that does not require a support optimization oracle and, moreover, is projection-free. In the development process, new results are derived for the regularized linear minimization problem over sparse symmetric sets, which give additional means to identify optimal solutions for convex and concave objective functions. We complement our results with numerical examples. [ABSTRACT FROM AUTHOR]