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Short-step methods are an important class of algorithms for solving convex constrained optimization problems. In this short paper, we show that under very mild assumptions on the self-concordant barrier and the width of the ℓ 2 -neighbourhood, any short-step interior-point method is not strongly polynomial-time. [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]

In recent years, distributed optimization problem have a wide range of applications in various fields. This paper considers the prescribed-time distributed optimization problem with/without constraints. Firstly, we assume the state of each agent is constrained, and the prescribed-time distributed optimization algorithm with constraints is designed on the basis of gradient projection algorithm and consensus algorithm. Secondly, the constrained distributed optimization problem is transformed into the unconstrained distributed optimization problem, and according to the gradient descent algorithm and consensus algorithm, we also propose the prescribed-time distributed optimization algorithm without constraints. By designing the appropriate objective functions, we prove the multi-agent system can converge to the optimal solution within any prescribed-time, and the convergence time is fully independent of the initial conditions and system parameters. Finally, three simulation examples are provided to verify the validity of the designed algorithms. • For distributed optimization problem with convex constraints, we design an effective prescribed-time distributed algorithm which can guarantee the multi-agent system converge to the optimal solution. • The designed algorithm in this paper can achieve convergence within any prescribed-time, and the convergence time is fully independent of the initial conditions and system parameters. • In this paper, we not only consider the condition that the agents' states are constrained, but also ensure that the multi-agent system can reach the optimal solution within any prescribed-time, which is more practical. [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]

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]

Motivation Understanding causal effects is a fundamental goal of science and underpins our ability to make accurate predictions in unseen settings and conditions. While direct experimentation is the gold standard for measuring and validating causal effects, the field of causal graph theory offers a tantalizing alternative: extracting causal insights from observational data. Theoretical analysis has shown that this is indeed possible, given a large dataset and if certain conditions are met. However, biological datasets, frequently, do not meet such requirements but evaluation of causal discovery algorithms is typically performed on synthetic datasets, which they meet all requirements. Thus, real-life datasets are needed, in which the causal truth is reasonably known. In this work we first construct such a large-scale real-life dataset and then we perform on it a comprehensive benchmarking of various causal discovery methods. Results We find that the PC algorithm is particularly accurate at estimating causal structure, including the causal direction which is critical for biological applicability. However, PC does only produces cause-effect directionality, but not estimates of causal effects. We propose PC-NOTEARS (PCnt), a hybrid solution, which includes the PC output as an additional constraint inside the NOTEARS optimization. This approach combines PC algorithm's strengths in graph structure prediction with the NOTEARS continuous optimization to estimate causal effects accurately. PCnt achieved best aggregate performance across all structural and effect size metrics. Availability and implementation https://github.com/zhu-yh1/PC-NOTEARS. [ABSTRACT FROM AUTHOR]

This contribution discusses the influence of different barrier update strategies on the performance and robustness of an interior point algorithm for single-crystal plasticity at small strains. To this end, single-crystal plasticity is first briefly presented in the framework of a primal-dual interior point algorithm to outline the general algorithmic structure. The manner in which the barrier parameter is modified within the interior point method, steering the penalization of constraints, plays a crucial role for the robustness and efficiency of the overall algorithm. In this paper, we compare and analyze different strategies in the framework of crystal plasticity. In a thorough analysis of a numerical example covering a broad range of settings in monocrystals, we investigate robust hyperparameter ranges and identify the most efficient and robust barrier parameter update strategies. [ABSTRACT FROM AUTHOR]

The use of evolutionary algorithms to solve constrained multi-objective optimization problems (CMOPs) with various characteristics and difficulties obtains considerable attention. Most of existing methods tend to introduce an alternate formulation to simplify the original problem and facilitate the solving, which corresponds to the methodology of multiform optimization. Inspired by multiform optimization, this paper proposes a multi-stage multiform optimization framework to solve CMOPs. To prevent the population from falling into local optima in the early stages of evolution, we construct an alternate formulation that ignores all constraints. Meanwhile, in order to utilize high-quality infeasible solutions to explore more feasible regions, we construct another alternate formulation by using a constraint relaxation technique that analyzes the relationships between constraints, evaluating important constraints, and ignoring unimportant constraints. The two formulations provide exclusive and complementary searches in the objective space with the help of knowledge transfer. As both alternate formulations are designed to find the unconstrained Pareto front in the early stages and the final goal must be finding the constrained Pareto front, a multi-stage strategy is devised. Different numbers of alternate formulations are used at different stages to allocate computational resources more effectively. In addition, we propose a hybrid operator strategy to improve the performance of the algorithm by combining the advantages of different operators. Then, 33 instances and 18 real-world CMOPs are selected to evaluate the performance of the algorithm. Experimental results demonstrate the superiority or competitiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

Deploying unmanned aerial vehicle base stations (UAV-BSs) to provide wireless access for terrestrial users is an alternative solution in emergency scenarios. Due to the dynamic nature of UAV-BSs and strong line-of-sight (LoS) transmission, co-frequency networking worsens the interference suffered by edge users, while the use of fully orthogonal channels for all UAV-BSs also faces the problem of frequency resource constraints. This paper develops a new deployment scheme by combining multiple UAV-BS locations, limited frequency reuse and power optimization. Thus, the nonlinear constrained optimization model is proposed to maximize user coverage. To reduce the computational complexity, the basic multi-UAV-BS network layout is first determined by polycentric clustering and connectivity adjustment based on user location distribution. Then, a genetic algorithm is used to optimize the multi-UAV-BS frequency arrangement and power adjustment to obtain the model solution. Simulations verify the effectiveness of the proposed scheme and evaluate the impact of co-channel interference. [ABSTRACT FROM AUTHOR]

In this paper, a numerical approximation method is developed to find approximate solutions to a class of constrained multi-objective optimization problems. All the functions of the problem are not necessarily convex functions. At each iteration of the method, a particular type of subproblem is solved using the trust region technique, and the step is evaluated using the notions of actual reduction and predicted reduction. A non-differentiable $ l_{\infty } $ l∞ penalty function restricts the constraint violations. An adaptive BFGS update formula is introduced. Global convergence of the proposed algorithm is established under the Mangasarian-Fromovitz constraint qualification and some mild assumptions. Furthermore, it is justified that the proposed algorithm displays a super-linear convergence rate. Numerical results are provided to show the efficiency of the algorithm in the quality of the approximated Pareto front. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze an away-step Frank–Wolfe algorithm designed for solving multiobjective optimization problems over polytopes. We prove that each limit point of the sequence generated by the algorithm is a weak Pareto optimal solution. Furthermore, under additional conditions, we show linear convergence of the whole sequence to a Pareto optimal solution. Numerical examples illustrate a promising performance of the proposed algorithm in problems where the multiobjective Frank–Wolfe convergence rate is only sublinear. [ABSTRACT FROM AUTHOR]

In this paper, we discuss how to use the Dantzig–Wolfe (DW) decomposition method to solve a class of constrained variational inequality (VI) problems. These problems include multi-regional energy equilibrium models with linking constraints or nonlinear multicommodity network flow problems with asymmetric cost functions and side constraints. The decomposed VI problem has a subproblem which is a constrained optimisation problem consisting of all structural constraints. The resulting master problem is a VI problem with dummy linking constraints. The size of the master problem is much smaller than that of the original constrained VI problem. If the subproblem comprises the constraint set with a special structure, such as block-angular structure, it can be further decomposed by the DW decomposition method (nested DW). We find that by performing an iteration of the nested DW decomposition on the subproblem (truncated DW), we can obtain an equilibrium solution. The efficiency of this truncated DW may depend on the VI problems. Theoretical analysis indicated that the algorithm is guaranteed to converge under some assumptions. Illustrative examples are given. From the results of the examples, we find that moving the linking constraints of the structural constraints back from the subproblem to the master problem may worsen the computational performance. [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]

Constrained multitasking optimization (CMTO) obtains increasing attention recently. The goal of CMTO is to handle multiple constrained tasks simultaneously. There are two limitations of existing studies on CMTO: (i) existing knowledge transfer techniques for CMTO may not work due to non-intersecting feasible domains and the unconsidered relationship between constraints and objectives; and (ii) knowledge diversity is lacking in existing CMTO algorithms because the representation of knowledge is biased to feasible solutions. To address these limitations, this paper proposes a co-evolution and domain adaptation (CEDA) method for CMTO. First, a new constraint relaxation-based domain adaptation technique for knowledge transfer is devised. Domain adaptation can effectively address the limitations imposed by non-intersecting feasible domains. In addition, as the population evolves, the knowledge representation is biased to different kinds of solutions. Second, a co-evolutionary strategy is proposed to improve the knowledge diversity. The two proposed techniques are with generality and can be readily integrated into different multitasking frameworks. In this paper, the CEDA method is combined with two popular multitasking (i.e., multifactorial-based and multi-population-based) frameworks. The constructed CEDA-based algorithms are compared with fifteen state-of-the-art algorithms on a CMTO benchmark suite and a real-world application. Experimental results demonstrate the superiority of the proposed CEDA method. [ABSTRACT FROM AUTHOR]

The flight environment of aerodynamically controlled missiles is full of complexity and uncertainty. To cope with the uncertainty more effectively and enhance the convergence performance in trajectory optimization problems for aerodynamically controlled missiles simultaneously, the chance-constrained sequential convex programming (CC-SCP) algorithm is proposed in this paper. The uncertainty is regarded as the chance constraint, and a smooth and differential approximation function is designed to transform this chance constraint into the constraint that the convex optimization method can handle. Subsequently, the originally non-convex trajectory optimization problem is reformulated into a series of convex optimization subproblems, in which an initial reference trajectory guess generation strategy is proposed, and a theoretical proof of the exact convex relaxation is given to enhance the algorithm's convergence performance and theoretical value, respectively. Numerical simulations are provided to verify the convergence and effectiveness of the CC-SCP algorithm, and the advantages of using the CC-SCP algorithm to cope with the uncertainty are illustrated. Furthermore, comparative simulation examples show that the proposed algorithm possesses a low conservatism, which means the proposed algorithm can obtain a bigger convergence region and a better solution than other current methods when handling the same chance constraints. Finally, the robustness of the algorithm is discussed. • The algorithm can handle the trajectory optimization problem with uncertainties. • The algorithm outperforms other current methods when handling the chance constraints. • A theoretical proof is given for the exact convex relaxation. [ABSTRACT FROM AUTHOR]

The key to solving constrained multiobjective optimization problems (CMOPs) lies in maintaining the feasibility, convergence, and diversity of the population. In recent years, various constraint handling techniques (CHTs) and strategies have been proposed to enhance the performance of constrained multiobjective evolutionary algorithms (CMOEAs). However, most of these algorithms face difficulties in dealing with problems that have large infeasible regions and discontinuous small feasible regions, as they have trouble crossing large infeasible regions while simultaneously maintaining the convergence and diversity of the population. To tackle this issue, this paper proposes a dual-population auxiliary coevolutionary algorithm with an enhanced operator, denoted as DAEAEO. Auxiliary population 1 employs an improved ϵ -constraint handling technique to provide high-quality feasible solutions for the main population. Auxiliary population 2 adopts the non-dominated sorting method to provide favorable objective information for the main population to help it cross the infeasible region. In addition, to further improve diversity, each population adopts an enhanced operator and a genetic operator to generate offspring, respectively. Finally, knowledge transfer between offspring is realized. Compared to six state-of-the-art CMOEAs on DASCMOPs, LIR-CMOPs, DOC test suites, and two real-world problems, the proposed DAEAEO achieved superior performance, especially for CMOPs with large infeasible regions and discontinuous small feasible regions. • A constrained multiobjective coevolutionary algorithm is proposed, termed DAEAEO. • A dual-population auxiliary evolutionary strategy is proposed. • The use of knowledge transfer promotes information interaction among offspring. • An enhanced search operator is developed to balance convergence and diversity. • The effectiveness of DAEAEO is verified on test suites and two real-world problems. [ABSTRACT FROM AUTHOR]

Many surrogate-assisted evolutionary algorithms (SAEAs) have been shown excellent search performance in solving expensive constrained optimization problems (ECOPs) with continuous variables, but few of them focus on ECOPs with mixed-integer variables (ECOPs-MI). Hence, a population state-driven surrogate-assisted differential evolution algorithm (PSSADE) is proposed for solving ECOPs-MI, in which the adaptive population update mechanism (APUM) and the collaborative framework of global and local surrogate-assisted search (CFGLS) are combined effectively. In CFGLS, a probability-driven mixed-integer mutation (PMIU) is incorporated into the classical global DE/rand/2 and local DE/best/2 for improving the diversity and potentials of candidate solutions, respectively, and the collaborative framework further integrates both the superiority of global and local mutation for the purpose of achieving a good balance between exploration and exploitation. Moreover, the current population is adaptively reselected based on the efficient non-dominated sorting technique in APUM when the population distribution is too dense. Empirical studies on 10 benchmark problems and 2 numerical engineering cases demonstrate that the PSSADE shows a more competitive performance than the existing state-of-the-art algorithms. More importantly, PSSADE provides excellent performance in the design of infrared stealth material film. [ABSTRACT FROM AUTHOR]

Several constrained optimization problems have been adequately solved over the years thanks to the advances in the area of metaheuristics. Nevertheless, the question as to which search logic performs better on constrained optimization often arises. In this paper, we present Dual Search Optimization (DSO), a co-evolutionary algorithm that includes an adaptive penalty function to handle constrained problems. Compared to other self-adaptive metaheuristics, one of the main advantages of DSO is that it is able auto-construct its own perturbation logics, i.e., the ways solutions are modified to create new ones during the optimization process. This is accomplished by co-evolving the solutions (encoded as vectors of integer/real values) and perturbation strategies (encoded as Genetic Programming trees), in order to adapt the search to the problem. In addition to that, the adaptive penalty function allows the algorithm to handle constraints very effectively, yet with a minor additional algorithmic overhead. We compare DSO with several algorithms from the state-of-the-art on two sets of problems, namely: (1) seven well-known constrained engineering design problems and (2) the CEC 2017 benchmark for constrained optimization. Our results show that DSO can achieve state-of-the-art performances, being capable to automatically adjust its behavior to the problem at hand. [ABSTRACT FROM AUTHOR]

This paper introduces an improved differential evolution algorithm based on cooperative multi-population (CMp-DE for short), which combines diverse population collaboration mechanisms and catalytic factors into an improved differential evolution framework. By harnessing various population collaboration mechanisms, the algorithm enhances the diversity of individuals within populations during initial iterations and reduces it during later iterations, thereby harmonizing the algorithm's exploratory and exploitative capabilities. Furthermore, a novel mutation operator is proposed that divides the iterative process into exploration and exploitation phases, thereby augmenting the algorithm's global exploration prowess. Lastly, a catalytic operator is introduced to generate new individuals near post-crossover individuals based on a specified rule, which enhances the algorithm's ability to escape local optima and increasing stability. The proposed CMp-DE is benchmarked against the CEC2017 benchmark test functions and compared against 13 algorithms, including five differential evolution algorithms and their variants, as well as eight state-of-the-art metaheuristic optimization algorithms. This evaluation assesses the CMp-DE's solution accuracy, convergence, stability, and scalability. Finally, the applicability of CMp-DE is validated by addressing six practical optimization problems. The experimental results show that CMp-DE surpasses other algorithms in terms of both convergence accuracy and robustness. Moreover, integrating a catalytic operator with other optimization algorithms notably boosts performance in convergence accuracy and stability. The inclusion of the catalytic operator has significantly enhanced the performance of algorithms compared to their performance before its addition. This underscores the potential of the catalytic operator in improving the performance of various algorithms, particularly in terms of convergence accuracy and robustness. [ABSTRACT FROM AUTHOR]

The optimization problems in a fluid catalytic cracking process with dynamic constraints and conflicting objectives are challenging due to the complicated constraints and dynamic environments. The decision variables need to be reoptimized to obtain the best objectives when dynamic environments arise. To solve these problems, we established a mathematical model and proposed a dynamic constrained multiobjective optimization evolution algorithm for the fluid catalytic cracking process. In this algorithm, we design an offspring generation strategy based on minimax solutions, which can explore more feasible regions and converge quickly. Additionally, a dynamic response strategy based on population feasibility is proposed to improve the feasible and infeasible solutions by different perturbations, respectively. To verify the effectiveness of the algorithm, we test the algorithm on ten instances based on the hypervolume metric. Experimental results show that the proposed algorithm is highly competitive with several state-of-the-art competitors. [ABSTRACT FROM AUTHOR]

The slime mould algorithm may not be enough and tends to trap into local optima, low population diversity, and suffers insufficient exploitation when real-world optimization problems become more complex. To overcome the limitations of SMA, the Gaussian mutation (GM) with a novel strategy is proposed to enhance SMA and it is named as SMA-GM. The GM is used to increase population diversity, which helps SMA come out of local optima and retain a robust local search capability. Additionally, the oscillatory parameter is updated and incorporated with GM to set the balance between exploration and exploitation. By using a greedy selection technique, this study retains an optimal slime mould position while ensuring the algorithm's rapid convergence. The SMA-GM performance was evaluated by using unconstrained, constrained, and CEC2022 benchmark functions. The results show that the proposed SMA-GM has a more robust capacity for global search, improved stability, a faster rate of convergence, and the ability to solve constrained optimization problems. Additionally, the Wilcoxon rank sum test illustrates that there is a significant difference between the optimization outcomes of SMA-GM and each compared algorithm. Furthermore, the engineering problem such as industrial refrigeration system (IRS), optimal operation of the alkylation unit problem, welded beam and tension/compression spring design problem are solved, and results prove that the proposed algorithm has a better optimization efficiency to reach the optimum value. [ABSTRACT FROM AUTHOR]

An optimization-based tool for flow predictions in natural rivers is introduced assuming that some physical characteristics of a river within a spatial-time domain [ x min , x max ] × [ t min , t today ] are known. In particular, it is assumed that the bed elevation and width of the river are known at a finite number of stations in [ x min , x max ] and that the flow-rate at x = x min is known for a finite number of time instants in [ t min , t today ] . Using these data, given t future > t today and a forecast of the flow-rate at x = x min and t = t future , a regression-based algorithm informed by partial differential equations produces predictions for all state variables (water elevation, depth, transversal wetted area, and flow-rate) for all x ∈ [ x min , x max ] and t = t future . The algorithm proceeds by solving a constrained optimization problem that takes into account the available data and the fulfillment of Saint-Venant equations for one-dimensional channels. The effectiveness of this approach is corroborated with flow predictions of a natural river. [ABSTRACT FROM AUTHOR]

Box-constrained optimization problems in the real m × n matrix space have been widely applied in big data mining. However, efficient solution of them is still a challenge. In this paper, a new nonmonotone line search rule is first proposed by extending the well-known ones and inheriting their advantages. Then, by analyzing and exploiting properties of this rule, a new nonmonotone spectral projected gradient algorithm is developed to solve the box-constrained optimization problems in the matrix space. Global convergence of the developed algorithm is also established. Numerical tests are conducted on a series of randomly generated test problems and those in the set of benchmark test problems. Compared with other existing nonmonotone line search rules, our rule shows its advantages in terms of the significantly reduced number of function evaluations and significantly reduced number of iterations. To further validate applicability of this research, we apply the studied optimization problem and the developed algorithm to solve the problems of image clustering. Numerical results demonstrate that the proposed method can generate better clustering results and is more robust than the similar ones available in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we propose an improved version of Twin SVM using a non-smooth optimization method. Twin SVM generally consists in determining two non-parallel planes by alternately solving two constrained optimization models. Solving this problem using the classical Lagrangian method has many limitations, notably: its only limited to handle Gaussian noise, generally exaggerates the influence of outliers and cannot handle unbalanced data, this due to the differentiability of the model. To circumvent these issues, we transform two-constraint optimization models using the penalty method into an unconstrained non-smooth optimization one. The non-smoothness nature of the problem has many advantages, but it requires special treatment, which is why we use the primal dual method to solve it, since it is the most appropriate and it is robust in terms of stability, convergence and speed (Lyaqini, Nachaoui and Hadri, 2022). To demonstrate the effectiveness of the proposed approach, several experiments were carried out on numerous UCI benchmarks, medical image and HandPD datasets. These experiments demonstrated the effectiveness and applicability of the proposed approach, with satisfactory results compared to the state of the art. [ABSTRACT FROM AUTHOR]

In this study, a novel meta-heuristic search (MHS) algorithm for constrained global optimization problems is proposed. Since many algorithms aim to achieve well-balanced exploitation–exploration stages with often unsatisfactory results, in the approach introduced in this paper, Attraction–Repulsion Optimization Algorithm (AROA), the balance associated with attraction–repulsion phenomena that occur in nature is mimicked. AROA introduces a search strategy in which a candidate solution is moved in the search space depending on the quality of solutions in its neighborhood, as well as the best candidate. The candidates are managed by local search operators based on modified Brownian motion, trigonometric functions, randomly selected solutions, and a form of memory. Consequently, AROA exhibits a satisfactory exploitation–exploration balance exhibited by highly competitive performance. The introduced algorithm is experimentally compared with the state-of-the-art meta-heuristics on the CEC 2014, 2017, and 2020 test suites. The obtained results reveal the advantages of AROA over related algorithms and its suitability in solving complex real-world problems. • A novel attraction–repulsion search scheme is introduced. • Proposed meta-heuristic is governed by balanced search operators. • Algorithm is validated on three demanding CEC benchmarks. [ABSTRACT FROM AUTHOR]

Model Predictive Control (MPC) has many advantages in controlling an aero-engine, such as handling actuator constraints, but the computational burden greatly obstructs its application. The current multiplex MPC can reduce computational complexity, but it will significantly decrease the control performance. To guarantee real-time performance and good control performance simultaneously, an intelligent reduced-dimensional scheme of MPC is proposed. The scheme includes a control variable selection algorithm and a control sequence coordination strategy. A constrained optimization problem with low computational complexity is first constructed by using only one control variable to define a reduced-dimensional control sequence. Therein, the control variable selection algorithm provides an intelligent mode to determine the control variable that has the best control effect at the current sampling instant. Furthermore, a coordination strategy is adopted in the reduced-dimensional control sequence to consider the interaction of control variables at different predicting instants. Finally, an intelligent reduced-dimensional MPC controller is designed and implemented on an aero-engine. Simulation results demonstrate the effectiveness of the intelligent reduced-dimensional scheme. Compared with the multiplex MPC, the intelligent reduced-dimensional MPC controller enhances the control quality significantly by 34.06%; compared with the standard MPC, the average time consumption is decreased by 64.72%. [ABSTRACT FROM AUTHOR]

Classical primal-dual algorithms attempt to solve max∣1 miι⅛ £(æ, μ) by alternately minimizing over the primal variable x through primal descent and maximizing the dual variable μ through dual ascent. However, when Z2(x, μ) is highly nonconvex with complex constraints in x, the minimization over x may not achieve global optimality and, hence, the dual ascent step loses its valid intuition. This observation motivates us to propose a new class of primal-dual algorithms for nonconvex constrained optimization with the key feature to reverse dual ascent to a conceptually new dual descent, in a sense, elevating the dual variable to the same status as the primal variable. Surprisingly, this new dual scheme achieves some best iteration complexities for solving nonconvex optimization problems. In particular, when the dual descent step is scaled by a fractional constant, we name it scaled dual descent (SDD), otherwise, unsealed dual descent (UDD). For nonconvex multiblock optimization with nonlinear equality constraints, we propose SDD-alternating direction method of multipliers (SDD-ADMM) and show that it finds an e-stationary solution in O{e~4) iterations. The complexity is further improved to O{e~3) and O{e~2) under proper conditions. We also propose UDD-augmented Lagrangian method (UDD-ALM), combining UDD with ALM, for weakly convex minimization over affine constraints. We show that UDD-ALM finds an e-stationary solution in O{e~2) iterations. These complexity bounds for both algorithms either achieve or improve the best-known results in the ADMM and ALM literature. Moreover, SDD-ADMM addresses a longstanding limitation of existing ADMM frameworks. [ABSTRACT FROM AUTHOR]

The dislocation hyperbolic augmented Lagrangian algorithm (DHALA) is a new approach to the hyperbolic augmented Lagrangian algorithm (HALA). DHALA is designed to solve convex nonlinear programming problems. We guarantee that the sequence generated by DHALA converges towards a Karush-Kuhn-Tucker point. We are going to observe that DHALA has a slight computational advantage in solving the problems over HALA. Finally, we will computationally illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

We present the Branch-and-Bound Performance Estimation Programming (BnB-PEP), a unified methodology for constructing optimal first-order methods for convex and nonconvex optimization. BnB-PEP poses the problem of finding the optimal optimization method as a nonconvex but practically tractable quadratically constrained quadratic optimization problem and solves it to certifiable global optimality using a customized branch-and-bound algorithm. By directly confronting the nonconvexity, BnB-PEP offers significantly more flexibility and removes the many limitations of the prior methodologies. Our customized branch-and-bound algorithm, through exploiting specific problem structures, outperforms the latest off-the-shelf implementations by orders of magnitude, accelerating the solution time from hours to seconds and weeks to minutes. We apply BnB-PEP to several setups for which the prior methodologies do not apply and obtain methods with bounds that improve upon prior state-of-the-art results. Finally, we use the BnB-PEP methodology to find proofs with potential function structures, thereby systematically generating analytical convergence proofs. [ABSTRACT FROM AUTHOR]

With the rapid growth in cellular user quantity and quality of service demand, the resource allocation in device-to-device communication system significantly affects the overall efficiency and user experience. In this study, the resource allocation for large-scale device-to-device communication system is modelled as a constrained optimization problem with thousands of dimensionalities. Then, the variable-coupling relationship of the developed model is analysed and the mathematical proof is firstly provided, and a novel algorithm namely multi-modal mutation cooperatively coevolving particle swarm optimization is developed to optimize the ultra-high dimensional model. Finally, efficacy of the developed method is verified by a comprehensive set of case studies, some famous algorithms for the specialized literature are also employed for comparison. Experimental results shown that the developed algorithm can obtain accurate and robust optimization performance for different system scales. In addition, when the system scale increases to 1000 cellular users and 300 D2D-pair users, the developed method can still outperform the compared algorithms and output accurate resource allocation solution. [ABSTRACT FROM AUTHOR]

In this paper, a randomized parallel algorithm is proposed to solve the distributed optimal consensus problem of multi-agent systems. Involving both the transient response and the final consensus state, the problem is described as a constrained non-separable optimization problem. Inspired by the randomized Jacobi proximal alternating direction method of multipliers, the proposed algorithm makes it possible for only a fraction of agents to solve their private subproblems in parallel at each iteration, which greatly saves computational resources and enhances running efficiency. The convergence analysis of the algorithm gives fully distributed convergence conditions. A trade-off between the convergence speed and resource savings is then obtained, where the convergence rate is estimated to be at least O 1 t . Furthermore, the algorithm can be accelerated to enjoy a convergence rate of O 1 t 2 by adaptively adjusting the auxiliary parameters properly. Numerical simulations demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

The cooperation of multi-agent systems (MAS) based on distributed model predictive control (DMPC) is a current research hotspot, and how to more effectively handle additive disturbances and reduce resource consumption are two difficult problems that need to be solved. In view of this, this paper aims to design a more effective DMPC strategy for MAS, so as to effectively deal with the above problems without loss of the control performance. Firstly, a finite-horizon constrained optimization problem is established for MAS, in which a robustness constraint is designed to effectively handle additive disturbances. Then, a new efficient event-triggering condition is designed, which is established by considering the mixed information of differential and integral of the state error. Furthermore, based on the dual-mode control, an event-triggered robust DMPC algorithm is proposed to further reduce the resource consumption of the system. In addition, theoretical results are provided through analysis and deduction to ensure the iterative feasibility of the algorithm, stability of the closed-loop system and Zeno-free behavior. Finally, the proposed algorithm is applied to two examples for simulation and comparison to verify its effectiveness. The simulation results show that compared to DMPC and classical event-triggered DMPC methods, the proposed algorithm can reduce the average resource consumption of MAS by more than 81% and 36%, respectively, which indicates that the proposed strategy can effectively reduce the computation and communication burden of MAS without affecting the control performance. [ABSTRACT FROM AUTHOR]