Inexact Newton Method for Solving Generalized Nash Equilibrium Problems

Abhishek Singh (), Debdas Ghosh () and Qamrul Hasan Ansari ()
Additional contact information
Abhishek Singh: Indian Institute of Technology (Banaras Hindu University)
Debdas Ghosh: Indian Institute of Technology (Banaras Hindu University)
Qamrul Hasan Ansari: Aligarh Muslim University

Journal of Optimization Theory and Applications, 2024, vol. 201, issue 3, No 15, 1333-1363

Abstract: Abstract In this article, we present an inexact Newton method to solve generalized Nash equilibrium problems (GNEPs). Two types of GNEPs are studied: player convex and jointly convex. We reformulate the GNEP into an unconstrained optimization problem using a complementarity function and solve it by the proposed method. It is found that the proposed numerical scheme has the global convergence property for both types of GNEPs. The strong BD-regularity assumption for the reformulated system of GNEP plays a crucial role in global convergence. In fact, the strong BD-regularity assumption and a suitable choice of a forcing sequence expedite the inexact Newton method to Q-quadratic convergence. The efficiency of the proposed numerical scheme is shown for a collection of problems, including the realistic internet switching problem, where selfish users generate traffic. A comparison of the proposed method with the existing semi-smooth Newton method II for GNEP is provided, which indicates that the proposed scheme is more efficient.

Keywords: Generalized Nash equilibrium problems; Player convex GNEP; Jointly convex GNEP; Complementarity functions; Inexact Newton method; BD-regularity (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-024-02411-8 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:201:y:2024:i:3:d:10.1007_s10957-024-02411-8

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

DOI: 10.1007/s10957-024-02411-8

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 ().