On approximate solutions in set-valued optimization problems
نویسندگان
چکیده
منابع مشابه
Lagrangian conditions for approximate solutions on nonconvex set-valued optimization problems
The purpose of this paper is to consider the set-valued optimization problem in Asplund spaces without convexity assumption. By a scalarization function introduced by Tammer and Weidner (J Optim Theory Appl 67:297–320, 1990), we obtain the Lagrangian condition for approximate solutions on set-valued optimization problems in terms of the Mordukhovich coderivative.
متن کاملApproximate Fenchel-Lagrangian Duality for Constrained Set-Valued Optimization Problems
In this article, we construct a Fenchel-Lagrangian ε-dual problem for set-valued optimization problems by using the perturbation methods. Some relationships between the solutions of the primal and the dual problems are discussed. Moreover, an ε-saddle point theorem is proved.
متن کاملOptimality conditions for various efficient solutions involving coderivatives: from set-valued optimization problems to set-valued equilibrium problems
In this paper, we present a new approach to the study of various efficient solutions of a set-valued equilibrium problem (for short, SEP) through the study of corresponding solutions of a set-valued optimization problem with a geometric constraint (for short, SOP). The solutions under consideration are: efficient solutions, weakly efficient solutions, strongly efficient solutions, and properly ...
متن کاملApproximate Solutions of Set-Valued Stochastic Differential Equations
In this paper, we consider the problem of approximate solutions of set-valued stochastic differential equations. We firstly prove an inequality of set-valued Itô integrals, which is related to classical Itô isometry, and an inequality of set-valued Lebesgue integrals. Both of the inequalities play an important role to discuss set-valued stochastic differential equations. Then we mainly state th...
متن کاملOn -optimality Conditions for Convex Set-valued Optimization Problems
In this paper, -subgradients for convex set-valued maps are defined. We prove an existence theorem for -subgradients of convex set-valued maps. Also, we give necessary optimality conditions for an -solution of a convex set-valued optimization problem (CSP). Moreover, using the single-valued function induced from the set-valued map, we obtain theorems describing the -subgradient sum formula for ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2012
ISSN: 0377-0427
DOI: 10.1016/j.cam.2012.04.012