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...
Main Authors: | , |
---|---|
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 |
_version_ | 1818325962394173440 |
---|---|
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. |
first_indexed | 2024-12-13T11:52:49Z |
format | Article |
id | doaj.art-48aee550e4b843989de3cc48a7383647 |
institution | Directory Open Access Journal |
issn | 1997-7670 2541-8785 |
language | English |
last_indexed | 2024-12-13T11:52:49Z |
publishDate | 2020-03-01 |
publisher | Irkutsk State University |
record_format | Article |
series | Известия Иркутского государственного университета: Серия "Математика" |
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 |
work_keys_str_mv | AT laltangerel anexactpenaltyapproachandconjugatedualityforgeneralizednashequilibriumproblemswithcouplingandsharedconstraints AT gbattur anexactpenaltyapproachandconjugatedualityforgeneralizednashequilibriumproblemswithcouplingandsharedconstraints AT laltangerel exactpenaltyapproachandconjugatedualityforgeneralizednashequilibriumproblemswithcouplingandsharedconstraints AT gbattur exactpenaltyapproachandconjugatedualityforgeneralizednashequilibriumproblemswithcouplingandsharedconstraints |