Exponential augmented Lagrangian methods for equilibrium problems. (2nd January 2022)

• Record Type: Journal Article
• Authors: Torrealba, E. M. R.; Matioli, L. C.; Nasri, M.; Castillo, R. A.
• Is Part Of: Optimization methods and software. Volume 37:Number 1(2022)
• Page Start: 295
• Page End: 319
• Publication Date: 2022-01-02
• Subjects: Augmented Lagrangian -- penalties -- Bregman distance -- proximal point method -- equilibrium problem -- Nash equilibrium problem; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2020.1751154
• Languages: English
• ISSNs: 1055-6788

Abstract

ABSTRACT: We introduce exponential augmented Lagrangian methods for solving equilibrium problems in finite-dimensional spaces, extending the so-called quadratic augmented Lagrangian methods. Unlike the quadratic augmented Lagrangian methods that are at most first-order differentiable, our exponential augmented Lagrangian methods can be differentiable at any order. Therefore, second-order methods, such as Newton's methods, can be used to solve the subproblems generated by the augmented Lagrangian methods. We also present numerical results obtained based on implementing our proposed algorithms in Matlab.