Existence Results for Noncoercive Mixed Variational Inequalities in Finite Dimensional Spaces

Alfredo Iusem; Felipe Lara

doi:10.1007/s10957-019-01548-1

Existence Results for Noncoercive Mixed Variational Inequalities in Finite Dimensional Spaces

Alfredo Iusem
, Felipe Lara

Institute of Higher Research

Instituto National de Matemática Pura e Aplicada

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

We use asymptotic analysis and generalized asymptotic functions for studying nonlinear and noncoercive mixed variational inequalities in finite dimensional spaces in the nonconvex case, that is, when the operator is nonlinear and noncoercive and the function is nonconvex and noncoercive. We provide general necessary and sufficient optimality conditions for the set of solutions to be nonempty and compact. As a consequence, a characterization of the nonemptiness and compactness of the solution set, when the operator is affine and the function is convex, is given. Finally, a comparison with existence results for equilibrium problems is presented.

Original language	English
Pages (from-to)	122-138
Number of pages	17
Journal	Journal of Optimization Theory and Applications
Volume	183
Issue number	1
DOIs	https://doi.org/10.1007/s10957-019-01548-1
State	Published - 15 Oct 2019

Keywords

Asymptotic analysis
Asymptotic functions
Equilibrium problems
Noncoercive optimization
Variational inequalities

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10.1007/s10957-019-01548-1

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title = "Existence Results for Noncoercive Mixed Variational Inequalities in Finite Dimensional Spaces",

abstract = "We use asymptotic analysis and generalized asymptotic functions for studying nonlinear and noncoercive mixed variational inequalities in finite dimensional spaces in the nonconvex case, that is, when the operator is nonlinear and noncoercive and the function is nonconvex and noncoercive. We provide general necessary and sufficient optimality conditions for the set of solutions to be nonempty and compact. As a consequence, a characterization of the nonemptiness and compactness of the solution set, when the operator is affine and the function is convex, is given. Finally, a comparison with existence results for equilibrium problems is presented.",

keywords = "Asymptotic analysis, Asymptotic functions, Equilibrium problems, Noncoercive optimization, Variational inequalities",

author = "Alfredo Iusem and Felipe Lara",

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T1 - Existence Results for Noncoercive Mixed Variational Inequalities in Finite Dimensional Spaces

AU - Iusem, Alfredo

AU - Lara, Felipe

PY - 2019/10/15

Y1 - 2019/10/15

N2 - We use asymptotic analysis and generalized asymptotic functions for studying nonlinear and noncoercive mixed variational inequalities in finite dimensional spaces in the nonconvex case, that is, when the operator is nonlinear and noncoercive and the function is nonconvex and noncoercive. We provide general necessary and sufficient optimality conditions for the set of solutions to be nonempty and compact. As a consequence, a characterization of the nonemptiness and compactness of the solution set, when the operator is affine and the function is convex, is given. Finally, a comparison with existence results for equilibrium problems is presented.

AB - We use asymptotic analysis and generalized asymptotic functions for studying nonlinear and noncoercive mixed variational inequalities in finite dimensional spaces in the nonconvex case, that is, when the operator is nonlinear and noncoercive and the function is nonconvex and noncoercive. We provide general necessary and sufficient optimality conditions for the set of solutions to be nonempty and compact. As a consequence, a characterization of the nonemptiness and compactness of the solution set, when the operator is affine and the function is convex, is given. Finally, a comparison with existence results for equilibrium problems is presented.

KW - Asymptotic analysis

KW - Asymptotic functions

KW - Equilibrium problems

KW - Noncoercive optimization

KW - Variational inequalities

UR - https://www.scopus.com/pages/publications/85067979847

U2 - 10.1007/s10957-019-01548-1

DO - 10.1007/s10957-019-01548-1

M3 - Article

AN - SCOPUS:85067979847

SN - 0022-3239

VL - 183

SP - 122

EP - 138

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 1

ER -

Existence Results for Noncoercive Mixed Variational Inequalities in Finite Dimensional Spaces

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Keywords

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