On the uniqueness of non-reducible multi-player control problems. (2nd November 2021)

• Record Type: Journal Article
• Authors: Karl, Veronika; Pörner, Frank
• Is Part Of: Optimization methods and software. Volume 36:Number 6(2021)
• Page Start: 1259
• Page End: 1288
• Publication Date: 2021-11-02
• Subjects: GNEP -- semi-smoothness -- Newton method -- variational inequality; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2019.1694021
• Languages: English
• ISSNs: 1055-6788

Abstract

ABSTRACT: In this article, we consider a special class of generalized Nash equilibrium problems that cannot be reduced to a single player control problem. We find a sufficient condition, that proves the existence and uniqueness of solutions. Problems of this type can be solved by a semi-smooth Newton method. Applying the same condition as needed for the uniqueness of solutions, we derive superlinear convergence for the associated Newton method and the equivalent active-set method. We also provide detailed finite element discretizations for both methods. Numerical examples are presented to support the theoretical findings.