共查询到20条相似文献,搜索用时 9 毫秒
1.
Convergence Results for Weak Efficiency in Vector Optimization Problems with Equilibrium Constraints
In this paper, we consider weak efficiency in vector
optimization problems with equilibrium constraints. We obtain
results on the convergence of the marginal map, the value, and the
solution sets.
This research was supported by Hong Kong Polytechnic University under Grant G-YY33 and by
National Science Foundation of China under Grant 10401043.
The authors express their gratitude to Professor Guangya Chen for careful reading of an earlier version of this paper. The authors are grateful to the anonymous referees for helpful comments and constructive suggestions. 相似文献
2.
In this article, necessary conditions of Fritz John type for weak efficient solutions of a nonsmooth vector equilibrium problem involving equilibrium constraints (VEPEC) in terms of the Clarke subdifferentials are established. Under constraint qualifications which are suitable for (VEPEC), necessary conditions of Kuhn-Tucker type for efficiency are derived. Under assumptions on generalized convexity of data, sufficient conditions for efficiency are developed. Some applications to vector variational inequalities and vector optimization problems with equilibrium constraints are also given. 相似文献
3.
Some Remarks On Vector Optimization Problems 总被引:6,自引:0,他引:6
K. R. Kazmi 《Journal of Optimization Theory and Applications》1998,96(1):133-138
We prove the existence of a weak minimum for vector optimization problems by means of a vector variational-like inequality and preinvex mappings. 相似文献
4.
Semicontinuity of Solution Mappings of Parametric Generalized Vector Equilibrium Problems 总被引:1,自引:0,他引:1
In this paper, we study the ε-generalized vector equilibrium problem (ε-GVEP) and the ε-extended vector equilibrium problem (ε-EVEP), which can be regarded as approximate problems to the generalized vector equilibrium problems (GVEP). Existence results
for ε-GVEP and ε-EVEP are established. We investigate also the continuity of the solution mappings of ε-GVEP and ε-EVEP. In particular, two results concerning the lower semicontinuity of the solution mappings of ε-GVEP and ε-EVEP are presented.
This research was partially supported by Grant NSC 95-2811-M-110-010. 相似文献
5.
α-Well-posedness for Nash Equilibria and For Optimization Problems with Nash Equilibrium Constraints
We present the concepts of α-well-posedness for parametric noncooperative games and for optimization problems with constraints defined by parametric Nash equilibria. We investigate some classes of functions that ensure these types of well-posedness and the connections with α-well-posedness for variational inequalities and optimization problems with variational inequality constraints. 相似文献
6.
T. Q. Bao P. Gupta B. S. Mordukhovich 《Journal of Optimization Theory and Applications》2007,135(2):179-203
We study multiobjective optimization problems with equilibrium constraints (MOPECs) described by parametric generalized equations
in the form
where both mappings G and Q are set-valued. Such models arise particularly from certain optimization-related problems governed by variational inequalities
and first-order optimality conditions in nondifferentiable programming. We establish verifiable necessary conditions for the
general problems under consideration and for their important specifications by using modern tools of variational analysis
and generalized differentiation. The application of the obtained necessary optimality conditions is illustrated by a numerical
example from bilevel programming with convex while nondifferentiable data. 相似文献
7.
The purpose of this paper is to study systems of vector equilibrium problems. We establish some existence theorems for systems
of vector equilibrium problems by using (S)+-conditions and Kakutani–Fan–Glicksberg fixed point theorem
*This work was supported by the Kyungnam University Research Fund 2004 相似文献
8.
Characterizations of Solutions for Vector Equilibrium Problems 总被引:5,自引:0,他引:5
Ansari Q.H. Konnov I.V. Yao J.C. 《Journal of Optimization Theory and Applications》2002,113(3):435-447
In this paper, we characterize the solutions of vector equilibrium problems as well as dual vector equilibrium problems. We establish also vector optimization problem formulations of set-valued maps for vector equilibrium problems and dual vector equilibrium problems, which include vector variational inequality problems and vector complementarity problems. The set-valued maps involved in our formulations depend on the data of the vector equilibrium problems, but not on their solution sets. We prove also that the solution sets of our vector optimization problems of set-valued maps contain or coincide with the solution sets of the vector equilibrium problems. 相似文献
9.
In this paper, we consider convergence properties of a class of penalization methods for a general vector optimization problem with cone constraints in infinite dimensional spaces. Under certain assumptions, we show that any efficient point of the cone constrained vector optimization problem can be approached by a sequence of efficient points of the penalty problems. We also show, on the other hand, that any limit point of a sequence of approximate efficient solutions to the penalty problems is a weekly efficient solution of the original cone constrained vector optimization problem. Finally, when the constrained space is of finite dimension, we show that any limit point of a sequence of stationary points of the penalty problems is a KKT stationary point of the original cone constrained vector optimization problem if Mangasarian–Fromovitz constraint qualification holds at the limit point.This work is supported by the Postdoctoral Fellowship of Hong Kong Polytechnic University. 相似文献
10.
A. Y. Azimov 《Journal of Optimization Theory and Applications》2008,137(1):61-74
The duality of multiobjective problems is studied with the help of the apparatus of conjugate set-valued mappings introduced
by the author. In this paper (Part 1), a duality theory is developed for set-valued mappings, which is then used to derive
dual relations for some general multiobjective optimization problems which include convex programming and optimal control
problems. Using this result, in the companion paper (Part 2), duality theorems are proved for multiobjective quasilinear and
linear optimal control problems. The theory is applied to get dual relations for some multiobjective optimal control problem. 相似文献
11.
The quasi-equilibrium problems with constraints are formulated and some sufficient conditions on the existence of their solutions are shown. As special cases, we obtain several results on the existence of solutions of some vector quasivariational inequality and vector optimization problems. An application of the obtained results is given to show the existence of solutions of quasi-optimization problems with constraints. 相似文献
12.
In this paper, approximate solutions of vector optimization problems are analyzed via a metrically consistent ε-efficient concept. Several properties of the ε-efficient set are studied. By scalarization, necessary and sufficient conditions for approximate solutions of convex and
nonconvex vector optimization problems are provided; a characterization is obtained via generalized Chebyshev norms, attaining
the same precision in the vector problem as in the scalarization.
This research was partially supported by the Ministerio de Educación y Ciencia (Spain), Project MTM2006-02629 and by the Consejería
de Educación de la Junta de Castilla y León (Spain), Project VA027B06. The authors are grateful to the anonymous referees
for helpful comments and suggestions. 相似文献
13.
We generalize stochastic mathematical programs with equilibrium constraints (SMPEC) introduced by Patriksson and Wynter (Ref. 1) to allow for the inclusion of joint upper-level constraints and to change the continuity assumptions with respect to the uncertainty parameters assumed before by measurability assumptions. For this problem, we prove the existence of solutions. We discuss also algorithmic aspects of the problem, in particular the construction of an inexact penalty function for the SMPEC problem. We apply the theory to the problem of structural topology optimization. 相似文献
14.
We consider a nonsmooth vector optimization continuous-time problem. We establish weak and strong duality theorems under generalized
convexity assumptions.
This research was supported by Center of Excellence for Mathematics, University of Isfahan, Isfahan, Iran. 相似文献
15.
Well-posedness for Optimization Problems with Constraints defined by Variational Inequalities having a unique solution 总被引:3,自引:0,他引:3
We introduce various notions of well-posedness for a family of variational inequalities and for an optimization problem with constraints defined by variational inequalities having a unique solution. Then, we give sufficient conditions for well-posedness of these problems and we present an application to an exact penalty method. 相似文献
16.
本文研究了集值映射向量优化问题的锥弱有效解的镇定性和稳定性,我们引进了集值映射向量优化问题的镇定性和稳定性的定义,并证明了集值映射向量优化问题的镇定性和稳定性的一些主要定理. 相似文献
17.
J. J. Júdice H. D. Sherali I. M. Ribeiro A. M. Faustino 《Journal of Optimization Theory and Applications》2007,134(3):467-481
In this paper, an algorithm for solving a mathematical programming problem with complementarity (or equilibrium) constraints
(MPEC) is introduced, which uses the active-set methodology while maintaining the complementarity restrictions throughout
the procedure. Finite convergence of the algorithm to a strongly stationary point of the MPEC is established under reasonable
hypotheses. The algorithm can be easily implemented by adopting any active-set code for nonlinear programming. Computational
experience is included to highlight the efficacy of the proposed method in practice. 相似文献
18.
In this paper, we study optimality conditions for vector optimization problems of a difference of convex mappings
where
is a closed convex cone in a Banach space Z, l is a mapping Q-convex from a Banach space X into Z, A is a continuous linear operator from X into a Banach space
and
are respectively the nonnegative orthants of
and
, C is a nonempty closed convex subset of X, b∈W, and the functions fi,gi,hj and kj are convex for i=1,...,p and j=1,ldots,m. Necessary optimality conditions for (VP) are established in terms of Lagrange-Fritz-John multipliers. When the set of constraints for (VP) is convex and under the generalized Slater constraint qualification introduced in Jeyakumar and Wolkowicz [11] , we derive necessary optimality conditions in terms of Lagrange-Karush-Kuhn-Tucker multipliers which are also sufficient whenever the functions gi,i=1,...,p are polyhedrals. Our approach consists in using a special scalarization function. A necessary optimality condition for convex vector maximization problem is derived. Also an application to vector fractional mathematical programming is given. Our contribution extends the results obtained in scalar optimization by Hiriart-Urruty [9] and improve substantially the few results known in vector case (see for instance: [11], [12] and [14]).Mathematics Subject Classification (1991). Primary: 90C29; Secondary 49K30 相似文献
19.
Equilibrium Problems with Applications to Eigenvalue Problems 总被引:5,自引:0,他引:5
In this paper, we consider equilibrium problems and introduce the concept of (S)+ condition for bifunctions. Existence results for equilibrium problems with the (S)+ condition are derived. As special cases, we obtain several existence results for the generalized nonlinear variational inequality studied by Ding and Tarafdar (Ref. 1) and the generalized variational inequality studied by Cubiotti and Yao (Ref. 2). Finally, applications to a class of eigenvalue problems are given. 相似文献
20.
César Gutiérrez Bienvenido Jiménez Vicente Novo 《Computational Optimization and Applications》2006,35(3):305-324
This work deals with approximate solutions in vector optimization problems. These solutions frequently appear when an iterative
algorithm is used to solve a vector optimization problem. We consider a concept of approximate efficiency introduced by Kutateladze
and widely used in the literature to study this kind of solutions. Necessary and sufficient conditions for Kutateladze’s approximate
solutions are given through scalarization, in such a way that these points are approximate solutions for a scalar optimization
problem. Necessary conditions are obtained by using gauge functionals while monotone functionals are considered to attain
sufficient conditions. Two properties are then introduced to describe the idea of parametric representation of the approximate
efficient set. Finally, through scalarization, characterizations and parametric representations for the set of approximate
solutions in convex and nonconvex vector optimization problems are proved and the obtained results are applied to Pareto problems.
AMS Classification:90C29, 49M37
This research was partially supported by Ministerio de Ciencia y Tecnología (Spain), project BFM2003-02194. 相似文献