Relaxation Methods for Generalized Nash Equilibrium Problems with Inexact Line Search

A. Heusinger () and C. Kanzow ()
Additional contact information
A. Heusinger: University of Würzburg
C. Kanzow: University of Würzburg

Journal of Optimization Theory and Applications, 2009, vol. 143, issue 1, No 10, 159-183

Abstract: Abstract The generalized Nash equilibrium problem (GNEP) is an extension of the standard Nash game where, in addition to the cost functions, also the strategy spaces of each player depend on the strategies chosen by all other players. This problem is rather difficult to solve and there are only a few methods available in the literature. One of the most popular ones is the so-called relaxation method, which is known to be globally convergent under a set of assumptions. Some of these assumptions, however, are rather strong or somewhat difficult to understand. Here, we present a modified relaxation method for the solution of a certain class of GNEPs. The convergence analysis uses completely different arguments based on a certain descent property and avoids some of the technical conditions for the original relaxation method. Moreover, numerical experiments indicate that the modified relaxation method performs quite well on a number of different examples taken from the literature.

Keywords: Generalized Nash equilibrium problem; Normalized Nash equilibrium; Relaxation method; Regularized Nikaido-Isoda function; Global convergence (search for similar items in EconPapers)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (11)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-009-9553-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:143:y:2009:i:1:d:10.1007_s10957-009-9553-0

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-009-9553-0

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().