Loading [MathJax]/jax/output/HTML-CSS/config.js
full
search.png

Search

close.png

Cancel

arrow
Volume 28, Issue 2
A Penalty Approach for Generalized Nash Equilibrium Problem

Jian Hou & Junfeng Lai

Commun. Math. Res., 28 (2012), pp. 181-192.

Published online: 2021-05

Preview Purchase PDF 2254 29538

Cited by

google scholar semantic scholar
Export citation
  • Abstract

The generalized Nash equilibrium problem (GNEP) is a generalization of the standard Nash equilibrium problem (NEP), in which both the utility function and the strategy space of each player depend on the strategies chosen by all other players. This problem has been used to model various problems in applications. However, the convergent solution algorithms are extremely scare in the literature. In this paper, we present an incremental penalty method for the GNEP, and show that a solution of the GNEP can be found by solving a sequence of smooth NEPs. We then apply the semismooth Newton method with Armijo line search to solve latter problems and provide some results of numerical experiments to illustrate the proposed approach.

  • Keywords

Nash equilibrium problem, generalized Nash equilibrium problem, logarithmic barrier function, quasi-variational inequality, semismooth Newton method.

  • AMS Subject Headings

90C30, 91A10, 91A80

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CMR-28-181, author = {Hou , Jian and Lai , Junfeng}, title = {A Penalty Approach for Generalized Nash Equilibrium Problem}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {28}, number = {2}, pages = {181--192}, abstract = {

The generalized Nash equilibrium problem (GNEP) is a generalization of the standard Nash equilibrium problem (NEP), in which both the utility function and the strategy space of each player depend on the strategies chosen by all other players. This problem has been used to model various problems in applications. However, the convergent solution algorithms are extremely scare in the literature. In this paper, we present an incremental penalty method for the GNEP, and show that a solution of the GNEP can be found by solving a sequence of smooth NEPs. We then apply the semismooth Newton method with Armijo line search to solve latter problems and provide some results of numerical experiments to illustrate the proposed approach.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19058.html} }
TY - JOUR T1 - A Penalty Approach for Generalized Nash Equilibrium Problem AU - Hou , Jian AU - Lai , Junfeng JO - Communications in Mathematical Research VL - 2 SP - 181 EP - 192 PY - 2021 DA - 2021/05 SN - 28 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19058.html KW - Nash equilibrium problem, generalized Nash equilibrium problem, logarithmic barrier function, quasi-variational inequality, semismooth Newton method. AB -

The generalized Nash equilibrium problem (GNEP) is a generalization of the standard Nash equilibrium problem (NEP), in which both the utility function and the strategy space of each player depend on the strategies chosen by all other players. This problem has been used to model various problems in applications. However, the convergent solution algorithms are extremely scare in the literature. In this paper, we present an incremental penalty method for the GNEP, and show that a solution of the GNEP can be found by solving a sequence of smooth NEPs. We then apply the semismooth Newton method with Armijo line search to solve latter problems and provide some results of numerical experiments to illustrate the proposed approach.

Hou , Jian and Lai , Junfeng. (2021). A Penalty Approach for Generalized Nash Equilibrium Problem. Communications in Mathematical Research . 28 (2). 181-192. doi:
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard