Making Augmented Lagrangian Methods Computer Amenable for Equilibrium Problems. (3rd June 2019)

• Record Type: Journal Article
• Authors: Nasri, Mostafa; Matioli, Luiz Carlos; Torrealba, Elvis Manuel Rodriguez
• Is Part Of: Optimization. Volume 68:Number 6(2019)
• Page Start: 1107
• Page End: 1130
• Publication Date: 2019-06-03
• Subjects: Augmented Lagrangian -- Equilibrium problem -- Nash equilibrium problem -- Newton method -- Subgradient projection method; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1576665
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: We develop three algorithms to solve the subproblems generated by the augmented Lagrangian methods introduced by Iusem-Nasri (2010) for the equilibrium problem. The first algorithm that we propose incorporates the Newton method and the other two are instances of the subgradient projection method. One of our algorithms is also capable of solving nondifferentiable equilibrium problems. Using well-known test problems, all algorithms introduced here are implemented and numerical results are reported to compare their performances.