On characterization of solution sets of set-valued pseudoinvex optimization problems
type: Item
instance of: scholarly article
title: On characterization of solution sets of set-valued pseudoinvex optimization problems
zbMATH Open document ID: 1322.90089
author: M. Oveisiha
author: Jafar Zafarani
published in: Journal of Optimization Theory and Applications
publication date: 2014-12-15T00:00:00Z
review text: The authors consider Stampaccia variational-like inequalities in terms of a normal subdifferential for set-valued maps. In Section 2, some basic definitions and preliminaries are given. Section 3 presents some relationships between Stampaccia variational-like inequalities and scalarized set-valued optimization problems. In particular, it is proven that any solution of a scalarized weak set-valued optimization problem is also a solution of the problem with Stampaccia variational-like inequalities (Theorem 3.1 and for real vector-valued functions, Theorem 3.2). In Section 4, some characterizations of the solution sets of set-valued optimization problems under the condition of pseudoinvexity are presented. The derived results hold also for the convex case which extends the results of earlier works.
reviewed by: Frank Werner
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 90C48
Mathematics Subject Classification ID: 49J27
Mathematics Subject Classification ID: 90C33
zbMATH DE Number: 6380436
zbMATH Keywords: set-valued map
zbMATH Keywords: normal subdifferential
zbMATH Keywords: Stampaccia variational-like inequality
zbMATH Keywords: solution set
MaRDI profile type: Publication
full work available at URL: s10957-013-0509-z
OpenAlex ID: W2116093930
cites work: Q3944358
cites work: Generalized Minty vector variational-like inequalities and vector optimization problems
cites work: Nonsmooth vector optimization problems and Minty vector variational inequalities
cites work: Q3840325
cites work: Vector optimization problem and generalized convexity
cites work: Generalized Minty vector variational-like inequalities and vector optimization problems in Asplund spaces
cites work: Vector optimization and variational-like inequalities
cites work: Vector variational-like inequality with pseudoinvexity
cites work: Recent Developments in Vector Optimization
cites work: Existence of weakly efficient solutions in nonsmooth vector optimization
cites work: Nonsmooth variational-like inequalities and nonsmooth vector optimization
cites work: A simple characterization of solutions sets of convex programs
cites work: On characterizing the solution sets of pseudolinear programs
cites work: On characterizing the solution sets of pseudoinvex extremum problems
cites work: Characterizations of the solution sets of pseudoinvex programs and variational inequalities
cites work: Generalized pseudolinearity
cites work: A note on characterizing solution set of nonsmooth pseudoinvex optimization problem
cites work: Characterizations of the nonemptiness and compactness for solution sets of convex set-valued optimization problems
cites work: Maximum principle in the problem of time optimal response with nonsmooth constraints
cites work: Q5325780
cites work: Necessary conditions for super minimizers in constrained multiobjective optimization
cites work: Relative Pareto minimizers for multiobjective problems: Existence and optimality conditions
cites work: Super efficient solutions for set-valued maps
cites work: Pre-invex functions in multiple objective optimization
cites work: On invex sets and preinvex functions
cites work: Vector optimization. Set-valued and variational analysis.
cites work: Characterizations of the solution set for a class of nonsmooth optimization problems
DOI: 10.1007/S10957-013-0509-Z
description: scientific article; zbMATH DE number 6380436