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Operations Research (OR) is a branch of applied mathematics that deals with optimization problems arising from different real contexts. The solving process of its problems is based on the construction and resolution of mathematical models, showing the possible connections between mathematics and the real world. Nevertheless, OR is not typically included in most curricula of higher secondary schools (i.e. Grades 9–12), but it is usually presented mainly at university level. To show how OR could be significant for these school students' education, the authors of this paper developed an educational project consisting of three teaching units. In this paper, we share the result of the teaching experiment related to the first unit, addressed to Grade 10. Qualitative and quantitative analyses show how it is appropriate to include OR and its typology of problems in regular school mathematics lectures. Second, these data also show how modelling and problem-solving skills, developed working with OR, can be fostered by implementing a collaborative way of working, also by making use of digital technologies. Last but not least, we demonstrate the positive impact such activities have on students' appreciation of OR. [ABSTRACT FROM AUTHOR]

The efficient design of the aerodynamic surfaces in the aircraft allows the optimal performance of the vehicle and the reduction of the fuel consumption. Among these surfaces, the wing is the main contributor to the force which lifts the aircraft enabling the flight. However, the application of this force out of the center of gravity generates a moment that must be balanced through a force applied in the Horizontal-Tail-Plane (HTP) reaching the longitudinal trim of the aircraft. Traditionally, the design of the wing and HTP have been performed iteratively attaining suboptimal or time ineffective results. In this paper, we solve this problem through the application of a Genetic Algorithm for the combined optimization of the wing and the HTP by adjusting the aspect ratio, the taper ratio, the twist angle and the incidence angle of both surfaces to produce the optimal balance of lift adjusting its distribution to an elliptical configuration and enabling the longitudinal trim. Results show the automatic adjustment of the parameters of the aerodynamic surfaces thus fulfilling the objectives of this paper. [ABSTRACT FROM AUTHOR]

In recent years, many studies have been used in feed-forward neural network (FNN) to develop decision-making systems. The primary objective is to get the least error by finding the best combination of control parameters. It has been observed that FNNs using meta-heuristics techniques always converges very quickly towards the optimal positions but suffers from slow searching speeds at later stages of generation. Due to slow convergence, it is a prevalent phenomenon that traditional optimization does not ensure to find global optima. As a result, it falls under local optima. Recently, another meta-heuristic optimization-based algorithm called sine cosine algorithms (SCA) was introduced to solve the aforementioned issues. The algorithm is fundamentally predicated on two trigonometric functions, one being sine and the other being cosine. However, like other traditional approaches, SCA has a tendency to be stuck in sub-optimal regions due to poor exploration and exploitation capabilities. This paper proposes an improved version of SCA named chaotic oppositional SCA (COSCA) by integrating with chaos theory and oppositional based learning into the SCA optimization process. It is an incipient training method employed to train an FNN. Three benchmark problems are used to examine the precision and performance of FNNs equipped with COSCA, COPSO, OSCA, SCA, PSO, and backpropagation. The experimental results showed that, relative to other meta-heuristic optimization techniques, the COSCA technique is able to improve performance. [ABSTRACT FROM AUTHOR]

Mixed pixels are the main reason for the low accuracy of traditional remote sensing applications. Hyperspectral image unmixing can explore the sub-pixel information of mixed pixels, which is an effective measure to solve the problems of low precision. Current unmixing methods only consider the correlation of local or global pixels and do not fully utilize images information. Based on the above problems, we proposed a novel sparse unmixing model named combining low-rank constrain for similar superpixels and total variation sparse unmixing (CLRSS-TV) in this current research paper. The adjacent similar pixels are clustered first into superpixels, then the superpixels with the same semantic information are merged into a collection. The spatial information of the image is fully considered by twice clustering. Weighted low-rank constraint is imposed on each collection to consider the spectral correlation of pixels. Moreover, the TV regularization and l2,1 norm are utilized to improve the smoothness and row sparsity, respectively. Experimental results reveal that the proposed method is not only competitive with the four state-of-the-art algorithms in simulated and actual datasets, but also has good anti-noise ability and universality. However, this paper still fails to overcome the problem of parameters selection in sparse unmixing, so the future work study intends to adopt the intelligent optimization algorithm to obtain the optimal parameters. [ABSTRACT FROM AUTHOR]

This paper considers the distributed cluster optimisation problem of multi-agent systems (MASs). Different from existing optimisation problems, the MASs are divided into several clusters, and each cluster has its own optimisation objective which is the sum of their local objective functions. Firstly, based on communication topology, the distributed optimisation problem with two clusters is considered and a kind of distributed control protocol is proposed. By using the fixed-time stability theory and the convexity of function, it is proved that the MASs can not only achieve cluster consensus in a fixed-time interval, but also solve the optimisation problem asymptotically. Secondly, the MASs with multiple clusters are further considered. We extend the proposed protocol to a more general case and also prove that MASs can achieve cluster consensus in fixed-time and asymptotically reach the optimal solution of the optimisation objective. Finally, some numerical simulations are presented to show the efficacy of the theoretical results. [ABSTRACT FROM AUTHOR]

Over the last two decades, the PageRank problem has received increased interest from the academic community as an efficient tool to estimate web-page importance in information retrieval. Despite numerous developments, the design of efficient optimization algorithms for the PageRank problem is still a challenge. This paper proposes three new algorithms with a linear time complexity for solving the problem over a bounded-degree graph. The idea behind them is to set up the PageRank as a convex minimization problem over a unit simplex, and then solve it using iterative methods with small iteration complexity. Our theoretical results are supported by an extensive empirical justification using real-world and simulated data. [ABSTRACT FROM AUTHOR]

The design of a trajectory is significant to the efficiency and safety of a drilling process. In this paper, wellbore stability, indicated by the safe mud weight, is introduced as constraints to formulate a drilling trajectory optimisation problem. The upper and lower bounds of the safe mud weight are analysed according to the real data of a well. To solve the optimisation problem with strict constraints, we devise a new multi-objective optimisation algorithm. The devised algorithm takes advantage of inverted generational distance and knee points, and improves the convergence and diversity of the obtained solutions by modifying the selection process. Simulation results show that the devised algorithm is effective on the drilling trajectory optimisation problem constrained to wellbore stability. [ABSTRACT FROM AUTHOR]

Economic Load Dispatch (ELD) is the most inherent necessity in power system operation to minimize the cost as well as the accomplishment of load demand abundantly. The main purpose of ELD is to satisfy load demand with the minimization of cost. Distinct techniques have been used for resolving the ELD problem. This paper introduces a robust and effective technique named Artificial Eco System Optimization (AEO) Algorithm to solve ELD. AEO is a population-based optimizer stimulated by the flow of energy into the Earth's ecosystem. This algorithm shows three distinct functions of living organisms, including production, consumption, and decomposition. By accomplishing three operator producer, consumer, and decomposer whole algorithm works and balances between the exploitation and the exploration phases of the technique. For solving the ELD problem, AEO has been implemented on multiple test systems with an account of different restrictions and AEO has given better results than different several novels, previous and hybrid optimization techniques. The outcomes confirm the robustness, expediency, effectiveness, and efficacy of AEO in terms of computational time and vicinity to the global optimum solution. [ABSTRACT FROM AUTHOR]

In this paper, proper minimal elements of a given nonconvex set in a real ordered Banach space are defined utilizing the limiting (Mordukhovich) normal cone. The newly defined points are called limiting proper minimal (LPM) points. It is proved that each LPM is a proper minimal in the sense of Borwein under some assumptions. The converse holds in Asplund spaces. The relation of LPM points with Benson, Henig, super and proximal proper minimal points are established. Under appropriate assumptions, it is proved that the set of robust elements is a subset of the set of LPM points, and the set of LPM points is dense in that of minimal points. Another part of the paper is devoted to scalarization-based and distance function-based characterizations of the LPM points. The paper is closed by some results about LPM solutions of a set-valued optimization problem via variational analysis tools. Clarifying examples are given in addition to the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we generalize Darvay’s technique for linear programming tohorizontal linear complementarity problem over the Cartesian product of symmetric cones, or briefly Cartesian-SCHLCP, using Euclidean Jordan algebras. This problem is a comprehensive optimization problem over symmetric cones, so that handling this problem removes the necessity of dealing with many other ones. This paper is among the first ones which study interior point methods (IPMs) for the generic Cartesian-SCHLCP problems. The symmetrization of the search directions used in this paper is based on the Nesterov–Todd (NT) scaling scheme, and only full-NT steps are used at each iteration. So, line searches are not longer needed. The derived complexity bound matches the best obtained one for infeasible IPMs with small updates. [ABSTRACT FROM AUTHOR]

This paper studies multiobjective optimal control problems in presence of constraints in the discrete time framework. Both the finite- and infinite-horizon settings are considered. The paper provides necessary conditions of Pareto optimality under lighter smoothness assumptions compared to the previously obtained results. These conditions are given in the form of weak and strong Pontryagin principles which generalize the existing ones. To obtain some of these results, we provide new multiplier rules for multiobjective static optimization problems and new Pontryagin principles for the finite horizon multiobjective optimal control problems. [ABSTRACT FROM AUTHOR]

In this paper, we present a feasible predictor-corrector interior-point method for symmetric cone optimization problem in the large neighbourhood of the central path. The method is generalization of Ai-Zhang's predictor-corrector algorithm to the symmetric cone optimization problem. Starting with a feasible point in given large neighbourhood of the central path, the algorithm still terminates in at most iterations. This matches the best known iteration bound that is usually achieved by short-step methods, thereby, closing the complexity gap between long- and short-step interior-point methods for symmetric cone optimization. The preliminary numerical results on a selected set of NETLIB problems show advantage of the method in comparison with the version of the algorithm that is not based on the predictor-corrector scheme. [ABSTRACT FROM AUTHOR]

The paper is devoted to the study of a bilevel multiobjective optimization problems with objectives and constraints given as differences of convex functions. The main attention is paid to deriving sufficient optimality conditions. Several intermediate optimization problems are introduced to help us in our investigation. [ABSTRACT FROM AUTHOR]

Most of the metaheuristics can efficiently solve unconstrained problems; however, their performance may degenerate if the constraints are involved. This paper proposes two constraint handling approaches for an emerging metaheuristic of Cohort Intelligence (CI). More specifically CI with static penalty function approach (SCI) and CI with dynamic penalty function approach (DCI) are proposed. The approaches have been tested by solving several constrained test problems. The performance of the SCI and DCI have been compared with algorithms like GA, PSO, ABC, d-Ds. In addition, as well as three real world problems from mechanical engineering domain with improved solutions. The results were satisfactory and validated the applicability of CI methodology for solving real world problems. [ABSTRACT FROM AUTHOR]

In this paper, we study a vector optimization problem (VOP) with both inequality and equality constraints. We suppose that the functions involved are Fréchet differentiable and their Fréchet derivatives are continuous or stable at the point of study. By virtue of a second-order constraint qualification of Abadie type, we provide second-order Karush-Kuhn-Tucker type necessary optimality conditions for the VOP. Moreover, we also obtain second-order sufficient optimality conditions for a kind of strict local efficiency. Both the necessary conditions and the sufficient conditions are shown in equivalent pairs of primal and dual formulations by using theorems of the alternative for the VOP. [ABSTRACT FROM AUTHOR]

Selecting an appropriate structure for a linear mixed model serves as an appealing problem in a number of applications such as in the modelling of longitudinal or clustered data. In this paper, we propose a variable selection procedure for simultaneously selecting and estimating the fixed and random effects. More specifically, a profile log-likelihood function, along with an adaptive penalty, is utilized for sparse selection. The Newton-Raphson optimization algorithm is performed to complete the parameter estimation. By jointly selecting the fixed and random effects, the proposed approach increases selection accuracy compared with two-stage procedures, and the usage of the profile log-likelihood can improve computational efficiency in one-stage procedures. We prove that the proposed procedure enjoys the model selection consistency. A simulation study and a real data application are conducted for demonstrating the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper studies partially observed risk-sensitive optimal control problems with correlated noises between the system and the observation. It is assumed that the state process is governed by a continuous-time Markov regime-switching jump-diffusion process and the cost functional is of an exponential-of-integral type. By virtue of a classical spike variational approach, we obtain two general maximum principles for the aforementioned problems. Moreover, under certain convexity assumptions on both the control domain and the Hamiltonian, we give a sufficient condition for the optimality. For illustration, a linear-quadratic risk-sensitive control problem is proposed and solved using the main results. As a natural deduction, a fully observed risk-sensitive maximum principle is also obtained and applied to study a risk-sensitive portfolio optimization problem. Closed-form expressions for both the optimal portfolio and the corresponding optimal cost functional are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the stability of the sets of (weak) minimal points and (weak) efficient points of vector optimization problems. Assuming that the objective functions are (strictly) properly quasi convex, and the data ofthe approximate problems converges to the data of the original problems in the sense of Painlevé–Kuratowski, we establish the Painlevé–Kuratowski set convergence of the sets of (weak) minimal points and (weak) efficient points of the approximate problems to the corresponding ones of original problem. Our main results improve and extend the results of the recent papers. [ABSTRACT FROM PUBLISHER]

In the present paper, a solution approach to fuzzy bilevel optimization problem is given for the linear case. We use-cuts of the fuzzy polytopes to attack the fuzzy optimization problem on upper level. Then, crisp optimization problems arise. Thus, the solution of the fuzzy upper level problem turns out to be a union of the solutions of these crisp problems on all-cuts. The solution approach for the lower level fuzzy optimization problem was investigated by the author in previous publications and is implemented in the present paper. [ABSTRACT FROM PUBLISHER]

In many mathematical models with complex parameter functions, it is critical to suggest a strategy for estimating those functions. This paper considers the problem of fitting parameter functions to given data by using a finite number of piecewise functions. Here, the primary aim is to propose several necessary and sufficient conditions that can guarantee the existence of parameter functions. With these criteria, the paper provides an algorithm for solving the parameter estimation problem efficiently. Numerical examples verify that the proposed algorithm is effective in estimating parameter functions in differential equations. [ABSTRACT FROM AUTHOR]

Motivated by the recent work of Mordukhovich et al. [Subgradients of marginal functions in parametric mathematical programming. Math. Program. Ser. B. 2009;116:369–396] on the optimal value function in parametric programming under inclusion constraints, this paper presents some new results on differential stability of convex optimization problems under inclusion constraints and functional constraints in Hausdorff locally convex topological vector spaces. By using the Moreau–Rockafellar theorem and appropriate regularity conditions, we obtain formulas for computing the subdifferential and the singular subdifferential of the optimal value function. By virtue of the convexity, several assumptions used in the above paper by Mordukhovich et al., like the nonemptyness of the Fréchet upper subdiffential of the objective function, the existence of a local upper Lipschitzian selection of the solution map, as well as the-inner semicontinuity and the-inner semicompactness of the solution map, are no longer needed. Relationships between our results and the corresponding ones in Aubin’s book [Optima and equilibria. An introduction to nonlinear analysis. 2nd ed. New York (NY): Springer; 1998] are discussed. [ABSTRACT FROM PUBLISHER]

In this paper, based on a new smoothing function, the general box constrained variational inequalities are solved by a smoothing Newton algorithm with a nonmonotone line search. The proposed algorithm is proved to be globally and locally superlinearly convergent under suitable assumptions. The preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonsmooth vector optimization problem involving locally Lipschitz generalized approximate convex functions and find some relations between approximate convexity and generalized approximate convexity. We establish relationships between vector variational inequalities and nonsmooth vector optimization problem using the generalized approximate convexity as a tool. [ABSTRACT FROM AUTHOR]

In this paper we consider stopping problems for continuous-time Markov chains under a general risk-sensitive optimization criterion for problems with finite and infinite time horizon. More precisely our aim is to maximize the certainty equivalent of the stopping reward minus cost over the time horizon. We derive optimality equations for the value functions and prove the existence of optimal stopping times. The exponential utility is treated as a special case. In contrast to risk-neutral stopping problems it may be optimal to stop between jumps of the Markov chain. We briefly discuss the influence of the risk sensitivity on the optimal stopping time and consider a special house selling problem as an example. [ABSTRACT FROM AUTHOR]

Multi-verse optimization algorithm (MVO) is one of the recent meta-heuristic optimization algorithms. The main inspiration of this algorithm came from multi-verse theory in physics. However, MVO like most optimization algorithms suffers from low convergence rate and entrapment in local optima. In this paper, a new chaotic multi-verse optimization algorithm (CMVO) is proposed to overcome these problems. The proposed CMVO is applied on 13 benchmark functions and 7 well-known design problems in the engineering and mechanical field; namely, three-bar trust, speed reduce design, pressure vessel problem, spring design, welded beam, rolling element-bearing and multiple disc clutch brake. In the current study, a modified feasible-based mechanism is employed to handle constraints. In this mechanism, four rules were used to handle the specific constraint problem through maintaining a balance between feasible and infeasible solutions. Moreover, 10 well-known chaotic maps are used to improve the performance of MVO. The experimental results showed that CMVO outperforms other meta-heuristic optimization algorithms on most of the optimization problems. Also, the results reveal that sine chaotic map is the most appropriate map to significantly boost MVO’s performance. [ABSTRACT FROM AUTHOR]

The 0–1 knapsack problem (KP) is a well-known intractable optimization problem with wide range of applications. Harmony Search (HS) is one of the most popular metaheuristic algorithms to successfully solve 0–1 KPs. Nevertheless, metaheuristic algorithms are generally compute intensive and slow when implemented in software. In this paper, we present an FPGA-based pipelined hardware accelerator to reduce computation time for solving large dimension 0–1 KPs using Binary Harmony Search algorithm. The proposed architecture exploits the intrinsic parallelism of population based metaheuristic algorithm and the flexibility and parallel processing capabilities of FPGAs to perform the computation concurrently thus enhancing performance. To validate the efficiency of the proposed hardware accelerator, experiments were conducted using a large number of 0–1 KPs. Comparative analysis on experimental results reveals that the proposed approach offers promising speedups of 51×– 111×as compared with a software implementation and 2×– 5×as compared with a hardware implementation of Binary Particle Swarm Optimization algorithm. Hardware Accelerator Implementation using Binary Harmony Search [ABSTRACT FROM AUTHOR]

For economical and efficient use of local multi-carrier energy systems, energy hubs (EHs) were introduced as the best solution. EHs as one type of distributed generation have made the use of multi-carrier energy systems attractive with better energy conservation. To achieve the economic and environmental objectives of the EH, the sizes of its components need to be optimally selected. In addition, to check the incentive of the EH, it must be studied under operation. For this reason, the economic dispatch of the EH is to be carried out. However, the two objectives of optimal design and optimal dispatch have been previously addressed as two separate problems one step after another. In this paper, a double-layer firefly based optimization algorithm is proposed to both optimally size and dispatch the EH components, simultaneously. The two problems are combined in one multi-objective optimization problem. The objectives are to minimize the total capital and operational cost of the EH, minimize the system emission, and maximize the cost of exported energy to the network. The proposed algorithm is effectively applied to a commercial facility (hospital) as a case study. [ABSTRACT FROM PUBLISHER]

This paper proposes an iterative strategy employing the linear programming (LP) method for the design of an all-pass variable-phase (AP-VP) digital filter in the minimax error sense. Mathematically, designing an AP-VP digital filter belongs to a non-linear optimisation problem. The novel LP design method first reduces this non-linear minimisation problem to a linear minimisation problem and then solves the linearised optimisation problem iteratively via using the LP method. The iterative LP-solving scheme is able to reduce the largest design errors significantly and thus can get a considerable accuracy improvement as compared to the noniterative one. We will utilise three design examples to show that this iterative scheme can get much better design results (much smaller maximum errors) than the noniterative method in the literature. Therefore, this iterative LP design strategy can significantly enhance the performance of the AP-VP digital filter. [ABSTRACT FROM AUTHOR]

Since complexity and scale of systems are continuously increasing, there is a growing interest in developing distributed algorithms that are capable to address information constraints, specially for solving optimisation and decision-making problems. In this paper, we propose a novel method to solve distributed resource allocation problems that include lower bound constraints. The optimisation process is carried out by a set of agents that use a communication network to coordinate their decisions. Convergence and optimality of the method are guaranteed under some mild assumptions related to the convexity of the problem and the connectivity of the underlying graph. Finally, we compare our approach with other techniques reported in the literature, and we present some engineering applications. [ABSTRACT FROM AUTHOR]

The paper describes a method for solving multi-objective optimization problems with box constraints. Unlike existing approaches, the proposed method not only constructs a finite approximation of Pareto frontier, but also proves its ϵ-optimality. The paper gives a detailed explanation of basic theoretical concepts behind the method and describes the algorithmic implementation. A practically important application of the proposed method to finding the working space of a robotic manipulator is presented. [ABSTRACT FROM AUTHOR]

This paper presents a newly deployed server, Interactive Dynamic Optimization Server (IDOS), devoted to solving optimal control problems. Development and deployment of the Interactive Dynamic Optimization Server is a result of a project funded by NCBiR (National Center for Research and Development in Poland) under grant R02-0009-06 (henceforth called briefly theIDOSproject). The aim of the project was to develop a prototype, online-accessible environment providing the service of solving dynamic optimization problems. One of the goals of the project was also to propose a modelling language (Dynamic Optimization Modelling Language,DOML) for defining optimal control problems – in a way that would not depend on constructs borrowed from concrete (lower level) programming languages. As a result, a user can specify his problem in a programming-language-neutral manner and use the server to attempt to solve it. The paper presents the workings of the server, the modelling language proposed (DOML) and an example of a problem specified inDOMLand solved withIDOS. [ABSTRACT FROM AUTHOR]

The efficiency of the classic alternating direction method of multipliers has been exhibited by various applications for large-scale separable optimization problems, both for convex objective functions and for nonconvex objective functions. While there are a lot of convergence analysis for the convex case, the nonconvex case is still an open problem and the research for this case is in its infancy. In this paper, we give a partial answer on this problem. Specially, under the assumption that the associated function satisfies the Kurdyka–Łojasiewicz inequality, we prove that the iterative sequence generated by the alternating direction method converges to a critical point of the problem, provided that the penalty parameter is greater than 2L, whereLis the Lipschitz constant of the gradient of one of the involved functions. Under some further conditions on the problem's data, we also analyse the convergence rate of the algorithm. [ABSTRACT FROM AUTHOR]

This paper studies linear non-increasing processing times and the common/slack due window assignment problems on a single machine, where the actual processing time of a job is a linear non-increasing function of its starting time. The aim is to minimize the sum of the earliness cost, tardiness cost, due window location and due window size. Some optimality results are discussed for the common/slack due window assignment problems and two O(nlogn) time algorithms are presented to solve the two problems. Finally, two examples are provided to illustrate the correctness of the corresponding algorithms. [ABSTRACT FROM PUBLISHER]

This paper presents a numerical scheme for solving fractional optimal control. The fractional derivative in this problem is in the Riemann–Liouville sense. The proposed method, based upon the method of moments, converts the fractional optimal control problem to a semidefinite optimization problem; namely, the nonlinear optimal control problem is converted to a convex optimization problem. The Grunwald–Letnikov formula is also used as an approximation for fractional derivative. The solution of fractional optimal control problem is found by solving the semidefinite optimization problem. Finally, numerical examples are presented to show the performance of the method. [ABSTRACT FROM AUTHOR]

The Barzilai–Borwein (BB) gradient method has received many studies due to its simplicity and numerical efficiency. By incorporating a nonmonotone line search, Raydan (SIAM J Optim. 1997;7:26–33) has successfully extended the BB gradient method for solving general unconstrained optimization problems so that it is competitive with conjugate gradient methods. However, the numerical results reported by Raydan are poor for very ill-conditioned problems because the effect of the degree of nonmonotonicity may be noticeable. In this paper, we focus more on the nonmonotone line search technique used in the global Barzilai–Borwein (GBB) gradient method. We improve the performance of the GBB gradient method by proposing an adaptive nonmonotone line search based on the morphology of the objective function. We also prove the global convergence and the R-linear convergence rate of the proposed method under reasonable assumptions. Finally, we give some numerical experiments made on a set of unconstrained optimization test problems of the CUTEr collection. The results show the efficiency of the proposed method in the sense of the performance profile introduced (Math Program. 2002;91:201–213) by Dolan and Moré. [ABSTRACT FROM AUTHOR]

In this paper, we consider the optimization problem in locally convex Hausdorff topological vector spaces with objectives given as the difference of two composite functions and constraints described by an arbitrary (possibly infinite) number of convex inequalities. Using the epigraph technique, we introduce some new constraint qualifications, which completely characterize the Farkas lemma, the dualities between the primal problem and its dual problem. Applications to the conical programming with DC composite function are also given. [ABSTRACT FROM AUTHOR]

In this paper, first, we show that the following optimization problem always has an optimal solution which does not depend on the matrix norm, and give a sufficient condition for the uniqueness of optimal solutions:(Section.Display) whereis any unitarily invariant norm,, andor. Then, we characterize the optimal solutions and also give sufficient conditions for the uniqueness and the rank-one property of optimal solutions for the following optimization problem:(Section.Display) where, is the inner product of matrices;,,, and’s,are different arbitrary norms. [ABSTRACT FROM AUTHOR]

This paper presents a new bi-objective mixed integer programming model for the two-stage assembly flow shop scheduling problem with preventive maintenance (PM) activities, in which the reliability/availability approach is employed to model the maintenance concepts of a problem. PM activities carry out the operations on machines and tools before the breakdown takes place. Therefore, it helps to prevent failures before they happen. After developing a new bi-objective model, an Epsilon-constraint method is proposed to solve the problem. This problem has been known as Np-hard. Therefore, three multi-objective optimization methods, namely fast non-dominated sorting genetic algorithm, Multi-objective imperialist competitive algorithm, and non-dominated ranking genetic algorithm (NRGA) are employed to find the pareto-optimal front for large sized problems. The parameters of the proposed algorithms are calibrated using artificial neural network (ANN) and the performances of the proposed algorithms on the problems of various sizes are analyzed and the computational results reveal that NRGA outperform than two other proposed algorithms in quality of solutions and computational time. [ABSTRACT FROM AUTHOR]

This paper solves a utility maximization problem under utility-based shortfall risk constraint, by proposing an approach using Lagrange multiplier and convex duality. Under mild conditions on the asymptotic elasticity of the utility function and the loss function, we find an optimal wealth process for the constrained problem and characterize the bi-dual relation between the respective value functions of the constrained problem and its dual. This approach applies to both complete and incomplete markets. Moreover, the extension to more complicated cases is illustrated by solving the problem with a consumption process added. Finally, we give an example of utility and loss functions in the Black–Scholes market where the solutions have explicit forms. [ABSTRACT FROM PUBLISHER]

Second-order necessary optimality conditions play an important role in optimization theory. This is explained by the fact that most numerical optimization algorithms reduce to finding stationary points satisfying first-order necessary optimality conditions. As a rule, optimization problems, especially the high dimensional ones, have a lot of stationary points so one has to use second-order necessary optimality conditions to exclude nonoptimal points. These conditions are closely related to second-order constraint qualifications, which guarantee the validity of second-order necessary optimality conditions. In this paper, strong and weak second-order necessary optimality conditions are considered and their validity proved under so-called critical regularity condition at local minimizers. [ABSTRACT FROM PUBLISHER]

This paper proposes techniques to improve the diversity of the searching points during the optimization process in an Aggregative Gradient-based Multiobjective Optimization (AGMO) method, so that well-distributed Pareto solutions are obtained. First to be discussed is a distance constraint technique, applied among searching points in the objective space when updating design variables, that maintains a minimum distance between the points. Next, a scheme is introduced that deals with updated points that violate the distance constraint, by deleting the offending points and introducing new points in areas of the objective space where searching points are sparsely distributed. Finally, the proposed method is applied to example problems to illustrate its effectiveness. [ABSTRACT FROM AUTHOR]

Where the most prevalent optimal servo-compensator formulations penalise the behaviour of an error system, this paper considers the problem of additionally penalising the actual states and inputs of the plant. Doing so has the advantage of enabling the penalty function to better resemble an economic cost. This is especially true of problems where control effort needs to be sensibly allocated across weakly redundant inputs or where one wishes to use penalties to soft-constrain certain states or inputs. It is shown that, although the resulting cost function grows unbounded as its horizon approaches infinity, it is possible to formulate an equivalent optimisation problem with a bounded cost. The resulting optimisation problem is similar to those in earlier studies but has an additional ‘correction term’ in the cost function, and a set of equality constraints that arise when there are redundant inputs. A numerical approach to solve the resulting optimisation problem is presented, followed by simulations on a micro–macro positioner that illustrate the benefits of the proposed servo-compensator design approach. [ABSTRACT FROM AUTHOR]

This paper aims at investigating the continuity of the efficient solution mapping of perturbed vector optimization problems. First, we introduce the concept of the level mapping. We give sufficient conditions for the upper semicontinuity and the lower semicontinuity of the level mapping. The upper semicontinuity and the lower semicontinuity of the efficient solution mapping are established by using the continuity properties of the level mapping. We establish a corollary about the lower semicontinuity of the minimal point set-valued mapping. Meanwhile, we give some examples to illustrate that the corollary is different from the ones in the literature. [ABSTRACT FROM PUBLISHER]

The aim of this paper is to design an efficient multigrid method for constrained convex optimization problems arising from discretization of some underlying infinite dimensional problems. Due to problem dependency of this approach, we only consider bound constraints with (possibly) a single equality constraint. As our aim is to target large-scale problems, we want to avoid computation of second derivatives of the objective function, thus excluding Newton-like methods. We propose a smoothing operator that only uses first-order information and study the computational efficiency of the resulting method. [ABSTRACT FROM AUTHOR]

In the practical business environment, portfolio managers often face business-driven requirements that limit the number of constituents in their tracking portfolio. A natural index tracking model is thus to minimize a tracking error measure while enforcing an upper bound on the number of assets in the portfolio. In this paper we consider such a cardinality-constrained index tracking model. In particular, we propose an efficient nonmonotone projected gradient (NPG) method for solving this problem. At each iteration, this method usually solves several projected gradient subproblems. We show that each subproblem has a closed-form solution, which can be computed in linear time. Under some suitable assumptions, we establish that any accumulation point of the sequence generated by the NPG method is a local minimizer of the cardinality-constrained index tracking problem. We also conduct empirical tests to compare our method with the hybrid evolutionary algorithm [P.R. Torrubiano and S. Alberto. A hybrid optimization approach to index tracking. Ann Oper Res. 166(1) (2009), pp. 57–71] and the hybrid half thresholding algorithm [F. Xu, Z. Xu and H Xue. Sparse index tracking: anregularization based model and solution, Submitted, 2012] for index tracking. The computational results demonstrate that our approach generally produces sparse portfolios with smaller out-of-sample tracking error and higher consistency between in-sample and out-of-sample tracking errors. Moreover, our method outperforms the other two approaches in terms of speed. [ABSTRACT FROM AUTHOR]

In the present paper, the issue of the optimal solving severely ill-posed problems is studied. The authors proposed projection scheme of discretization which is efficient with respect to the amount of used Galerkin information. By this scheme, the order-optimal estimates of quantities described information and algorithmic complexity are achieved. [ABSTRACT FROM AUTHOR]

In this paper, we study the well-posedness for the parametric optimization problems with variational inclusion problems as constraint (or the perturbed problem of optimization problems with constraint). Furthermore, we consider the relation between the well-posedness for the parametric optimization problems with variational inclusion problems as constraint and the well-posedness in the generalized sense for variational inclusion problems. [ABSTRACT FROM AUTHOR]

In this paper, the Wei–Yao–Liu (WYL) conjugate gradient projection algorithm will be studied for nonlinear monotone equations with convex constraints, which can be viewed as an extension of the WYL conjugate gradient method for solving unconstrained optimization problems. These methods can be applied to solving large-scale nonlinear equations due to the low storage requirement. We can obtain global convergence of our algorithm without requiring differentiability in the case that the equation is Lipschitz continuous. The numerical results show that the new algorithm is efficient. [ABSTRACT FROM AUTHOR]

In this paper, existence of critical point and weak efficient point of vector optimization problem is studied. A sequence of points in n-dimension is generated using positive definite matrices like Quasi-Newton method. It is proved that accumulation points of this sequence are critical points or weak efficient points under different conditions. An algorithm is provided in this context. This method is free from any kind of priori chosen weighting factors or any other form of a priori ranking or ordering information for objective functions. Also, this method does not depend upon initial point. The algorithm is verified in numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new numerical technique which we call fractional Chebyshev finite difference method. The algorithm is based on a combination of the useful properties of Chebyshev polynomial approximation and finite difference method. We implement this technique to solve numerically the non-linear programming problem which are governed by fractional differential equations (FDEs). The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the Caputo fractional derivatives. This operational matrix method can be regarded as a non-uniform finite difference scheme. The error bound for the fractional derivatives is introduced. The application of the method to the generated FDEs leads to algebraic systems which can be solved by an appropriate method. Two numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method. A comparison with the fourth-order Runge–Kutta method is given. [ABSTRACT FROM PUBLISHER]