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In this paper, the new short-term problems that are faced by a generation company in a deregulated electricity market are addressed and an optimization algorithm is proposed. Our model of the spot market explicitly represents the price of electricity as an uncertain exogenous variable. We consider a very complex problem of hydrothermal optimization with pumped-storage plants, so the problem deals with non-regular Lagrangian and non-holonomic inequality constraints. To obtain a necessary minimum condition, the problem was formulated within the framework of nonsmooth analysis using the generalized (or Clarke's) gradient and the Nonsmooth maximum principle. The optimal control problem is solved by means of an algorithm implemented in the commercial software package Mathematica. Results of the application of the method to a numerical example are presented. [ABSTRACT FROM AUTHOR]

This paper deals with a fully implicit time discretization scheme with variable time-step for a nonlinear system modelling phase transition and mechanical deformations in shape memory alloys. The model is studied in the non-stationary case and accounts for local microscopic interactions between the phases introducing the gradients of the phase parameters. The resulting initial-boundary value problem has already been studied by the author who proved existence, uniqueness and continuous dependence on data for a suitable weak solution along some regularity results. A careful and detailed investigation of the variable time-step discretization is the goal of this paper. Thus, we deduce some estimates for the discretization error. These estimates depend only on data, impose no constraints between consecutive time-steps and show an optimal order of convergence. Finally, we prove another regularity result for the solution under stronger regularity assumptions on data. [ABSTRACT FROM AUTHOR]

The r-component connectivity κ r (G) of the non-complete graph G is the minimum number of vertices whose deletion results in a graph with at least r components. So, κ2 is the usual connectivity. In this paper, we determine the r-component connectivity of the hypercube Q n for r=2, 3, …, n+1, and we classify all the corresponding optimal solutions. [ABSTRACT FROM PUBLISHER]

In this paper, we deal with the multiple-objective optimization problems, considering an improved definition of generalized type I univex function. Some optimality conditions as well as some duality relations are established. [ABSTRACT FROM AUTHOR]

This paper considers the problem of searching for the actual time of failure for a system when the only information that is available is that it is has failed by a time t. This situation can be analyzed by using the concept of the reversed failure rate. This paper considers optimization problems that can be solved by using the reversed failure rate. When a unit is detected to have failed at time t, we discuss an optimum backward time from time t to search for its failure time which minimizes the expected cost. The recovery of a database system and of reweighing products using a scale are taken to be two typical applications of the backward time concept. Two models are proposed for appropriate maintenance actions for these situations when a unit is detected to have failed at time t. [ABSTRACT FROM AUTHOR]

A continuous location problem in which a firm wants to set up a single new facility in a competitive environment is considered. Other facilities offering the same product or service already exist in the area. Both the location and the quality of the new facility are to be found so as to maximize the profit obtained by the firm. This is a hard-to-solve global optimization problem. An evolutionary algorithm called Universal Evolutionary Global Optimizer (UEGO) seems to be the best procedure to cope with it, but the algorithm needs several hours of CPU time for solving large instances. In this paper, four parallelizations of UEGO are presented. They all are coarse-grain methods which differ in their migratory policies. A computational study is carried out to compare the performance of the parallel algorithms. The results show that one of the parallelizations always gives the best objective function value and has an almost linear speed-up for up to 16 processing elements for large instances. [ABSTRACT FROM AUTHOR]

In this paper we present a new class of memory gradient methods for unconstrained optimization problems and develop some useful global convergence properties under some mild conditions. In the new algorithms, trust region approach is used to guarantee the global convergence. Numerical results show that some memory gradient methods are stable and efficient in practical computation. In particular, some memory gradient methods can be reduced to the BB method in some special cases. [ABSTRACT FROM AUTHOR]

In this paper, we study two types of approximate solutions for a vector optimization problem in Banach space setting. Our main concern is to define two new concepts of approximate saddle points and relate them to the above solution concepts. As a result, a dual is formulated, and duality results are established. [ABSTRACT FROM AUTHOR]

In this paper, we suggest a new version of the Gauss-Newton method for solving a system of non-linear equations which combines the idea of sharp merit function with the idea of quadratic regularization. For this scheme, we prove general convergence results and, under a natural non-degeneracy assumption, local quadratic convergence. We analyze the behavior of this scheme on a natural problem class for which we get global and local worst-case complexity bounds. The implementation of each step of the scheme can be done by standard convex optimization technique. [ABSTRACT FROM AUTHOR]

The combination of geometrically nonlinear analysis with structural optimization against instability opens many possibilities for new formulations of the optimization problem. One of them is optimization against instability in the large. When a critical state does not exist and instability occurs at finite displacements either the lower critical loading is maximized or the generalized displacement for that load is minimized. This paper undertakes these new optimization problems providing formulations and numerical solutions for selected elements. The simple finite dimensional model is analysed first showing characteristic features of the problem, and then a real elastic element is optimized. [ABSTRACT FROM AUTHOR]

In the paper, a new trust region algorithm is given for nonlinear inequality constrained optimization problems. Motivated by a dual problem introduced by Han and Mangasarian [Han, S. P., Mangasarian, O. L. (1983). A dual differentiable exact penalty function. Math. Programming 25:293-306], which is a nonnegatively constrained maximization problem, we construct a trust region algorithm for solving the dual problem. At each iteration, we only need to minimize a quadratic subproblem with simple bound constraints. Under the condition that the iterate sequence generated by the algorithm is contained in some bounded closed set, any accumulation point of the sequence is a Karush- Kuhn-Tucker point of the original problem. [ABSTRACT FROM AUTHOR]

The aim of this paper is to generalize the results of Yamada et al. [Yamada, I., Ogura, N., Yamashita, Y., Sakaniwa, K. (1998). Quadratic approximation of fixed points of nonexpansive mappings in Hilbert spaces. Numer. Funct. Anal. Optimiz. 19(l):165-190], and to provide complementary results to those of Deutsch and Yamada [Deutsch, F., Yamada, I. (1998). Minimizing certain convex functions over the intersection of the fixed point sets of nonexpansive mappings. Numer. Funct. Anal. Optim. 19(1&2):33-56] in which they consider the minimization of some function d over a closed convex set F, the nonempty intersection of N fixed point sets. We start by considering a quadratic function θ and providing a relaxation of conditions of Theorem 1 of Yamada et al. (1998) to obtain a sequence of fixed points of certain contraction maps, converging to the unique minimizer of θ over F. We then extend Theorem 2 and obtain a complementary result to Theorem 3 of Yamada et al. (1998) by replacing the condition lim n → ∞ (λn - λn+1)/λ²n+1 = 0 on the parameters by the more general condition lim n → ∞ λn / λn+1 = 1. We next look at minimizing a more general function θ than a quadratic function which was proposed by Deutsch and Yamada (1998) and show that the sequence of fixed points of certain maps converge to the unique minimizer of 9 over F. Finally, we prove a complementary result to that of Deutsch and Yamada (1998) by using the alternate condition on the parameters. [ABSTRACT FROM AUTHOR]

In the analysis of steel structures, several modern codes such as LRFD and Eurocode 3 provide for second-order approximate analysis. This paper presents a method of optimization for use in design that is directed toward improving the overall stability and strength of moment-resistant building frames. The method makes use of codified expressions for approximate second-order analysis. The objective function used in the optimization is the dominant eigenvalue of the linearized buckling problem. Only a first-order analysis is required, along with the calculation of the first eigenvalue of the linearized buckling problem of the structure. This new method provides a story by story procedure that is easily visualized. Several examples are provided to illustrate applications of the procedure. [ABSTRACT FROM AUTHOR]

Classification rules with a reserve judgment option provide a way to satisfy constraints on the misclassification probabilities when there is a high degree of overlap among the populations. Constructing rules which maximize the probability of correct classification while satisfying such constraints is a difficult optimization problem. This paper uses the form of the optimal solution to develop a relatively simple and computationally fast method for three populations which has a non parametric quality in controlling the misclassification probabilities. Simulations demonstrate that this procedure performs well. [ABSTRACT FROM AUTHOR]

The article explores the mechanics of the television game show "The Weakest Link." Contestants of the game answer general knowledge questions, with each correct answer raising the amount held in a temporary pot. The game involves several mathematical issues such as strategy optimization, existence of Nash equilibria, and voting considerations. The payoff vector as being the amount in the pot after a chain of correct answers was introduced to describe various versions of the game around the world.

In incomplete financial markets not every contingent claim can be replicated by a self-financing strategy. The risk of the resulting shortfall can be measured by convex risk measures, recently introduced by Föllmer and Schied (2002). The dynamic optimization problem of finding a self-financing strategy that minimizes the convex risk of the shortfall can be split into a static optimization problem and a representation problem. It follows that the optimal strategy consists in superhedging the modified claim [image omitted] , where H is the payoff of the claim and [image omitted] is a solution of the static optimization problem, an optimal randomized test. In this paper, necessary and sufficient optimality conditions are deduced for the static problem using convex duality methods. The solution of the static optimization problem turns out to be a randomized test with a typical 0-1-structure. [ABSTRACT FROM AUTHOR]

Direct search optimization algorithms are becoming an important alternative to well-established gradient based methods. Due to the fact that a single cost function evaluation may take a substantial amount of time, optimization can be a lengthy process. In order to shorten the run time one often resorts to parallel algorithms. Asynchronous algorithms are particularly efficient since they have no synchronization points. This paper is an attempt to establish a convergence theory for a class of such parallel direct search algorithms. The notion of a search direction generator (SDG) is introduced. An algorithmic framework for parallel distributed optimization methods based on SDGs is presented along with the corresponding convergence theory. The theory almost completely decouples the stepsize control from the sufficient descent requirement, which is necessary for the finite termination of the algorithm's inner loop. The proposed framework has several attributes considered very favourable in loosely coupled parallel systems (e.g. clusters of workstations), such as fault tolerance and scalability. The framework is illustrated by optimizing a set of test problems on a cluster of workstations. In all tested cases, a speedup was obtained that increased with the increasing number of workstations. Fault tolerance and scalability of the framework were also demonstrated by removing and adding workstations to the cluster while an optimization run was in progress. [ABSTRACT FROM AUTHOR]

In the procedure of steady-state hierarchical optimization for large-scale industrial processes, it is often necessary that the control system responds to a sequence of step function-type control decisions with distinct magnitudes. In this paper a set of iterative learning controllers are de-centrally embedded into the procedure of the steady-state optimization. This generates upgraded sequential control signals and thus improves the transient performance of the discrete-time large-scale systems. The convergence of the updating law is derived while the intervention from the distinction of the scales is analysed. Further, an optimal iterative learning control scheme is also deduced by means of a functional derivation. The effectiveness of the proposed scheme and the optimal rule is verified by simulation. [ABSTRACT FROM AUTHOR]

In this paper we investigate an optimal control problem for semilinear hyperbolic systems with unknown initial data. We first give some general existence results and then derive optimality conditions via a penalization method. Finally, we apply our abstract results to an example. [ABSTRACT FROM AUTHOR]

In this paper, a lead-to-pad alignment technique for surface mount component placement on printed circuit boards is developed. The problem is expressed as a nonlinear optimization problem with a linear objective function and quadratic constraints. A solution procedure is developed and compared with a known nonlinear optimization solution technique. Results show substantial improvements in execution time of the optimization and yield of the placement operation when implemented in a robotic cell. [ABSTRACT FROM AUTHOR]

Copyright of INFOR is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We consider nonlinear discrete optimal control problems with variable end points and with inequality and equality type constraints on trajectories and control. We derive first- and second-order necessary optimality conditions that are meaningful without a priori normality assumptions. [ABSTRACT FROM AUTHOR]

A new approach to a solution of a nonlinear constrained mathematical programming problem and its Mond-Weir duals is introduced. An n-approximated problem associated with a primal nonlinear programming problem is presented that involves n-approximated functions constituting the primal problem. The equivalence between the original mathematical programming problem and its associated n-approximated optimization problem is established under invexity assumption. Furthermore, n-approximated dual problems in the sense of Mond-Weir are introduced for the obtained n-approximated optimization problem in this method. By the help of n-approximated dual problems some duality results are established for the original mathematical programming problem and its original duals. [ABSTRACT FROM AUTHOR]

Suppose an experiment requires the fitting of a linear relationship Y = α + βX to data (xi, yi) where X and Y were both measured subject to error. In this paper a variety of methods are used to estimate the value of the slope β. Many popular methods are reformulated into a single class of optimization problems. Each method studied seeks to minimize a combination of the sum of the weighted deviations in the horizontal and vertical directions. The reformulation of each method is presented along with the results of a simulation study of the methods. [ABSTRACT FROM AUTHOR]

We study capacitated vehicle routing problems (CVRPs) in which the client demands occur over time and the collector or distributor performing the service can decide when to visit the clients. It has been reported in the literature that postponement of collection (or delivery) services may decrease the overall routing cost or distance. We investigate this issue in greater detail and report on experiments in different routing settings to uncover the impact of postponement on routing efficiency. We compare the results by a CVRP local search procedure with those obtained from an analytical, Continuous Approximation model. While the two approaches tend to generate similar results, the differences grow larger when the CVRPs' bin packing characteristics become more intricate. [ABSTRACT FROM AUTHOR]

Copyright of Professional Geographer is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this article, we develop a generalized proximal point algorithm for finding a weak Pareto optimal solution of minimizing an extended vector-valued map with respect to the positive orthant in finite-dimensional spaces by the virtue of a Bregman distance function. [ABSTRACT FROM AUTHOR]

We investigate the Extended Proximal Auxiliary Problem Principle (EPAPP) [A. Kaplan and R. Tichatschke, Extended Auxiliary Problem Principle using Bregman distances, Optimization 53 (2004), pp. 603-623, A. Kaplan and R. Tichatschke, Bregman functions and auxiliary problem principle, Optim. Methods Softw. 23, 1 (2008), pp. 95-107] for solving variational inequalities whose operator - here called the main operator - is the sum of a maximal monotone and a continuous operator. As usual for proximal methods using Bregman distances, Kalpan and Tichatschke required that the main operator is paramonotone. There are two main purposes of the present article. First, we establish the convergence of the EPAPP method without the use of paramonotonicity by replacing the latter assumption by other (partly rather natural) ones. An example showing that the main operator does not even have to be monotone is also given. Second, we discuss the EPAPP method with a stopping criterion of fixed-relative-error type by Solodov and Svaiter [An inexact hybrid generalized proximal point algorithm and some new results on the theory of Bregman functions, Math. Oper. Res. 25 (2000), pp. 214-230]. Kaplan and Tichatschke used a stopping criterion of summable-error type was used to admit an inexact solution of the corresponding auxiliary problems. To our knowledge, such a stopping criterion has not been applied to an extended APP yet; also in this situation, the paramonotonicity hypothesis is avoided. Independent of the stopping criterion under consideration, we admit an outer approximation of the set-valued component of the main operator. Owing to the use of Bregman-like functions to construct the symmetric components of the auxiliary operators, an interior-point effect is provided, meaning that - with a certain precaution - the auxiliary problems can be treated as unconstrained ones. [ABSTRACT FROM AUTHOR]

In this article, we investigate the optimal control problem governed by parabolic inclusion. We describe the Galerkin approximation and we demonstrate the existence of the strong condensation points of the set of solutions of approximate optimization problems. Each of these points is a solution of the initial optimization problem. [ABSTRACT FROM AUTHOR]

We give a lower semicontinuous type regularity condition and a closedness type one which turn out to be necessary and sufficient for the fulfilment of two different formulae involving the ε-subdifferential of a perturbation function, respectively. These regularity conditions prove to be sufficient also for having formulae for the classical subdifferential of a perturbation function. Some recently published results concerning ε-subdifferentials are rediscovered as special cases. [ABSTRACT FROM AUTHOR]

In this work, we study the structure of optimal solutions of infinite horizon autonomous variational problems with a lower semicontinuous integrand f : Rn × Rn → R1 ∪ {∞}, where Rn is the n-dimensional Euclidean space. We also show that all the optimality notions used in the literature are equivalent for the problems with the integrand f. [ABSTRACT FROM AUTHOR]

We study a nonsmooth vector optimization problem with an arbitrary feasible set or a feasible set defined by a generalized inequality constraint and an equality constraint. We assume that the involved functions are nondifferentiable. First, we provide some calculus rules for the contingent derivative in which the stability (a local Lipschitz property at a point) of the functions plays a crucial role. Second, another calculus rules are established for steady functions. Third, necessary optimality conditions are stated using tangent cones to the feasible set and the contingent derivative of the objective function. Finally, some necessary and sufficient conditions are presented through Lagrange multiplier rules. [ABSTRACT FROM AUTHOR]

The classes of reward-risk optimization problems that arise from different choices of reward and risk measures are considered. In certain examples the generic problem reduces to linear or quadratic programming problems. An algorithm based on a sequence of convex feasibility problems is given for the general quasi-concave ratio problem. Reward-risk ratios that are appropriate in particular for non-normal assets return distributions and are not quasi-concave are also considered. [ABSTRACT FROM AUTHOR]

In support set expansion sensitivity analysis, one concerns to find the range of parameter variation where the perturbed problem has an optimal solution with the support set that includes the support set of the given optimal solution of the unperturbed problem. In this article, we consider the perturbed convex quadratic optimization problem and present a method to identify the support set expansion sets for this problem. [ABSTRACT FROM AUTHOR]

Generally, global convergence of the conjugate gradient methods for unconstrained optimization problems needs Wolfe line search or strong Wolfe line search. In this article, we propose a cautious DY conjugate gradient method and prove that this method with Armijo line search converges globally if the objective function has Lipschitz continuous gradients. We also present some preliminary numerical results to show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

A substantial body of literature exists on the issues of optimization and scaling in HPLC. However, much of this literature is written in a theoretical manner such that it is difficult for the practicing chromatographer to apply the conclusions to problems in the laboratory. In addition, the analyst would have to search numerous publications to find all of the formulas that are needed when optimizing or scaling a method. In this review, an attempt is made to address these topics in a manner that is easy to follow, with all equations given in the form that is most convenient for the laboratory chemist, and with all necessary formulas available in a single source. The focus of the review is on the mathematical concepts relevant to optimization and scaling. Issues that are generally not approached mathematically, such as the selection of the mobile phase and stationary phase, are not discussed. [ABSTRACT FROM AUTHOR]

The article focuses on the structure theorem of the Jordan-Hölder-Schreier theorem. The structure is a generalization of the fundamental theorem of arithmetic which every integer is different from one or less than one decomposes into a product of primes. The Jordan-Hölder-Schreier theorem has the consequences that the simple factor groups that arise in the composition series are the same and occur with same multiplicity. The structure theorem simplifies the result which can be found for instance, the theorem asserts that it can refine each of the subnormal series which factor groups in the two resulting subnormal series can be paired so that corresponding factors are isomorphic.

This article presents a fuzzy multi-objective optimization model (FMOOM) for Volt/Var control within the frame of distribution management system (DMS) functions. Optimal control actions are of centralized character for the whole distribution system, based on historical operation database and available decentralized set of real-time measurements. Within the set of optimization goals/constraints, real power losses, overall voltage quality index and power factor are considered, with the possibility for the inclusion of other factors, without losing features of the FMOOM and calculation speed. To achieve an optimal defuzzified Volt/Var control solution with flexible input data, the robust technique of genetic algorithm (GA), is used. The application possibility of GA for the solution of real-time problems (like Volt/Var control) is explored. The aim is to give clear recommendations to decision-makers in view of setting GA control parameters that should ensure good quality of the near global optimal solution. The effectiveness of the proposed integrated GA–FMOOM for Volt/Var control, applied to various operation conditions, is verified on the example of a real radial distribution system from the Electric Power Industry of Serbia. [ABSTRACT FROM AUTHOR]

A practical active-set method for bound-constrained minimization is introduced. Within the current face the classical Euclidian trust-region method is employed. Spectral projected gradient directions are used to abandon faces. Numerical results are presented. [ABSTRACT FROM AUTHOR]

This article proposes a new multi-objective evolutionary algorithm, called neighbourhood exploring evolution strategy (NEES). This approach incorporates the idea of neighbourhood exploration together with other techniques commonly used in the multi-objective evolutionary optimization literature (namely, non-dominated sorting and diversity preservation mechanisms). The main idea of the proposed approach was derived from a single-objective evolutionary algorithm, called the line-up competition algorithm (LCA), and it consists of assigning neighbourhoods of different sizes to different solutions. Within each neighbourhood, new solutions are generated using a (1+?)-ES (evolution strategy). This scheme naturally balances the effect of local search (which is performed by the neighbourhood exploration mechanism) with that of the global search performed by the algorithm, and gradually impels the population to progress towards the true Pareto-optimal front of the problem to explore the extent of that front. Three versions of the proposal are studied: a (1+1)-NEES, a (1+2)-NEES and a (1+4)-NEES. Such approaches are validated on a set of standard test problems reported in the specialized literature. Simulation results indicate that, for continuous numerical optimization problems, the proposal (particularly the (1+1)-NEES) is competitive with respect to NSGA-II, which is an algorithm representative of the state-of-the-art in evolutionary multi-objective optimization. Moreover, all the versions of NEES improve on the results of NSGA-II when dealing with a discrete optimization problem. Although preliminary, such results might indicate a potential application area in which the proposed approach could be particularly useful. [ABSTRACT FROM AUTHOR]

In this article, we propose a method to identify contamination events (location and time of release) by enhancing a mathematical method originally proposed by Carasso et al. (Carasso, A., Sanderson, J.G. and Hyman, J.M., 1978, Digital removal of random media image degradation by solving the diffusion equation backward in time. SIAM Journal of Numerical Analysis, 15(4)). The method of the Marching-Jury Backward Beam/Plate Equation, applied earlier to groundwater problems, is enhanced and coupled to discrete Fourier transform processing techniques to solve a two-dimensional (2D) advection-dispersion transport problem with homogeneous and isotropic parameters backwards in time. (Atmadja, J. and Bagtzoglou, A.C., 2001a, Pollution source identification in heterogeneous porous media. Water Resources Research, 37(8), 2113–2125; Bagtzoglou, A.C. and Atmadja, J., 2003, The marching-jury backward beam equation and quasi-reversibility methods for hydrologic inversion: application to contaminant plume spatial distribution recovery. Water Resources Research, 39(2), 1038. Cornacchiulo, D. and Bagtzoglou, A.C., 2002, The marching-jury backward plate equation for contaminant plume spatial distribution recovery in two-dimensional heterogeneous media: Computational Issues, In: S.M. Hassanizadeh, R.J. Schotting, W.G. Gray and G.F. Pinder (Eds.) Computational Methods for Subsurface Flow and Transport (Netherlands: Elsevier Publishers) pp. 461–468. The difficulties associated with this ill-posed, inverse problem are well-recognized (Atmadja, J. and Bagtzoglou, A.C., 2001b, State-of-the-art report on mathematical methods for groundwater pollution source identification. Environmental Forensics, 2(3), 205–214). We, therefore, enhance the method by integrating an optimization scheme that takes as input parameters the stabilization parameter, the transport velocities, and the coefficient of diffusion. The objective function is set as an equally weighted sum of different mass and peak errors that can be calculated based on a combination of exhaustive contaminant coverage at specific points in time (e.g., lidar) and/or point data collected at a continuously monitored network of chemical sensors or biosensors, which may be stationary or mobile. [ABSTRACT FROM AUTHOR]

In sensitivity analysis one wants to know how the problem and the optimal solutions change under the variation of the input data. We consider the case when variation happens in the right-hand side of the constraints and/or in the linear term of the objective function. We are interested to find the range of the parameter variation in Convex Quadratic Optimization (CQO) problems where the support set of a given primal optimal solution remains invariant. This question has been first raised in Linear Optimization (LO) and known as Type II (so-called Support Set Invariancy ) sensitivity analysis. We present computable auxiliary problems to identify the range of parameter variation in support set invariancy sensitivity analysis for CQO. It should be mentioned that all the given auxiliary problems are LO problems and can be solved by an interior point method in polynomial time. We also highlight the differences between the characteristics of support set invariancy sensitivity analysis for LO and CQO. [ABSTRACT FROM AUTHOR]

This article concerns a new class of optimization-related problems called equilibrium problems with equilibrium constraints (EPEC). One may treat them as two-level hierarchical problems, which involve equilibria at both lower and upper levels. Such problems naturally appear in various applications providing an equilibrium counterpart (at the upper level) of mathematical programs with equilibrium constraints (MPEC). We develop a unified approach to both EPECs and MPECs from the viewpoint of multiobjective optimization subject to equilibrium constraints. The problems of this type are intrinsically nonsmooth and require the use of generalized differentiation for their analysis and applications. This article presents necessary optimality conditions for EPECs in finite-dimensional spaces based on advanced generalized differential tools of variational analysis. The optimality conditions are derived in normal form under certain qualification requirements, which can be regarded as proper analogs of the classical Mangasarian-Fromovitz constraint qualification in the general settings under consideration. [ABSTRACT FROM AUTHOR]

This article deals with the convergence (in the sense of Kuratowski-Painlevé) of the set of the minimal points of A n to the set of minimal points of A , whenever { A n } is a sequence of closed convex subsets of an Euclidean space, converging in the same sense to the set A . Next, we consider the convex vector optimization problem under the assumption that the objective function f is such that all its sublevel sets, restricted to the feasible region, are bounded. For this problem we investigate the convergence of the solution sets of perturbed (with respect to the feasible region and the objective function) problems both in the image space and in the decision space. We consider also the same topics for a linear problem. Finally, we apply our results to the study of stability for a vector programming problem with convex inequality and linear equality constraints. [ABSTRACT FROM AUTHOR]

A unified fixed point theoretic framework is proposed to investigate the asymptotic behavior of algorithms for finding solutions to monotone inclusion problems. The basic iterative scheme under consideration involves nonstationary compositions of perturbed averaged nonexpansive operators. The analysis covers proximal methods for common zero problems as well as for various splitting methods for finding a zero of the sum of monotone operators. [ABSTRACT FROM AUTHOR]

The aim of this article is to study necessary optimality conditions for a vector minimization program involving locally Lipschitz functions under certain general regularity conditions. We study problems involving only inequality and both inequality and equality constraints. [ABSTRACT FROM AUTHOR]

In this article, we present a new approach of hybrid simulated annealing method for minimizing multimodel functions called the simulated annealing heuristic pattern search (SAHPS) method. Two subsidiary methods are proposed to achieve the final form of the global search method, SAHPS. First, we introduce the approximate descent direction (ADD) method, which is a derivative-free procedure with high ability of producing a descent direction. Then, the ADD method is combined with a pattern search method with direction pruning to construct the heuristic pattern search (HPS) method. The last method is hybridized with simulated annealing (SA) to obtain the SAHPS method. The experimental results through well-known test functions are shown to demonstrate the efficiency of the proposed method SAHPS. [ABSTRACT FROM AUTHOR]

An extension of the auxiliary problem principle to variational inequalities with non-symmetric multi-valued operators in Hilbert spaces is studied. This extension supposes that the operator of the variational inequality is split up into the sum of a maximal monotone operator and a single-valued operator , which is linked with a sequence of non-symmetric components of auxiliary operators by a kind of pseudo Dunn property. The current auxiliary problem is constructed by fixing at the previous iterate, whereas is considered at a variable point. Using auxiliary operators of the form , the standard assumption of the strong convexity of the function h is weakened by exploiting mutual properties of and h . Convergence of the general scheme is analysed allowing that the auxiliary problems are solved approximately. Some applications are sketched briefly. [ABSTRACT FROM AUTHOR]

In this article, we present a method to obtain new Ekeland-type variational principles for mappings defined between locally convex spaces. The method is based on a special nuclear cone defined in a product of two locally convex spaces and on Pareto efficiency with respect to this cone. [ABSTRACT FROM AUTHOR]

Let X,Y be two Banach spaces, K ⊆ K be a nonempty set, C ⊆ Y be a pointed, closed, and convex cone, ϕ : K × K → Y and Φ : K × K × K → Y be two mappings. In this article, we consider the vector equilibrium problem: find x ∈ K such that for all y ∈ K , and the extended vector equilibrium problem: find x ∈ K such that for all y ∈ K . To study the above problems, we extend the classical ( S ) + -conditions to vectorial bifunctions. Under ( S ) + -conditions, we give some existence results for these two problems. [ABSTRACT FROM AUTHOR]