An Exact Penalty Approach and Conjugate Duality for Generalized Nash Equilibrium Problems with Coupling and Shared Constraints

Generalized Nash Equilibrium Problems (GNEP) have been attracted by many researchers in the field of game theory, operational research, engineering, economics as well as telecommunication in recent two decades. One of the most important classes of GNEP is a convex GNEP with jointly convex or shared...

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Main Authors: L. Altangerel, G. Battur
Format: Article
Language:English
Published: Irkutsk State University 2020-03-01
Series:Известия Иркутского государственного университета: Серия "Математика"
Subjects:
Online Access:http://mathizv.isu.ru/en/article/file?id=1338
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author L. Altangerel
G. Battur
author_facet L. Altangerel
G. Battur
author_sort L. Altangerel
collection DOAJ
description Generalized Nash Equilibrium Problems (GNEP) have been attracted by many researchers in the field of game theory, operational research, engineering, economics as well as telecommunication in recent two decades. One of the most important classes of GNEP is a convex GNEP with jointly convex or shared constraints which has been studied extensively. It is considered to be one of the most challenging classes of problems in the field. Moreover, there is a gap in the studies on the GNEP with coupling and shared constraints. The aim of this paper is to investigate the relationship between an exact penalty approach and conjugate duality in convex optimization for the GNEP with coupling and shared constraints. In association with necessary optimality conditions, we obtained the parameterized variational inequality problems. This problem has provided an opportunity to solve many other GNEs. Some numerical results are also presented.
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spelling doaj.art-48aee550e4b843989de3cc48a73836472022-12-21T23:47:18ZengIrkutsk State UniversityИзвестия Иркутского государственного университета: Серия "Математика"1997-76702541-87852020-03-01321316https://doi.org/10.26516/1997-7670.2020.32.3An Exact Penalty Approach and Conjugate Duality for Generalized Nash Equilibrium Problems with Coupling and Shared ConstraintsL. AltangerelG. BatturGeneralized Nash Equilibrium Problems (GNEP) have been attracted by many researchers in the field of game theory, operational research, engineering, economics as well as telecommunication in recent two decades. One of the most important classes of GNEP is a convex GNEP with jointly convex or shared constraints which has been studied extensively. It is considered to be one of the most challenging classes of problems in the field. Moreover, there is a gap in the studies on the GNEP with coupling and shared constraints. The aim of this paper is to investigate the relationship between an exact penalty approach and conjugate duality in convex optimization for the GNEP with coupling and shared constraints. In association with necessary optimality conditions, we obtained the parameterized variational inequality problems. This problem has provided an opportunity to solve many other GNEs. Some numerical results are also presented.http://mathizv.isu.ru/en/article/file?id=1338generalized nash equilibrium problemsexact penalty functionconjugate dualitycoupling and shared constraints
spellingShingle L. Altangerel
G. Battur
An Exact Penalty Approach and Conjugate Duality for Generalized Nash Equilibrium Problems with Coupling and Shared Constraints
Известия Иркутского государственного университета: Серия "Математика"
generalized nash equilibrium problems
exact penalty function
conjugate duality
coupling and shared constraints
title An Exact Penalty Approach and Conjugate Duality for Generalized Nash Equilibrium Problems with Coupling and Shared Constraints
title_full An Exact Penalty Approach and Conjugate Duality for Generalized Nash Equilibrium Problems with Coupling and Shared Constraints
title_fullStr An Exact Penalty Approach and Conjugate Duality for Generalized Nash Equilibrium Problems with Coupling and Shared Constraints
title_full_unstemmed An Exact Penalty Approach and Conjugate Duality for Generalized Nash Equilibrium Problems with Coupling and Shared Constraints
title_short An Exact Penalty Approach and Conjugate Duality for Generalized Nash Equilibrium Problems with Coupling and Shared Constraints
title_sort exact penalty approach and conjugate duality for generalized nash equilibrium problems with coupling and shared constraints
topic generalized nash equilibrium problems
exact penalty function
conjugate duality
coupling and shared constraints
url http://mathizv.isu.ru/en/article/file?id=1338
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