Optimization reformulations of the generalized Nash equilibrium problem using regularized indicator Nikaidô–Isoda function

• Published in: Journal of global optimization Vol. 57; no. 3; pp. 843 - 861
• Main Authors: Lalitha, C. S., Dhingra, Mansi
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.11.2013; Springer; Springer Nature B.V
• Subjects: Algorithms; Computer Science; Constraints; Equilibrium; Game theory; Indicators; Mathematical analysis; Mathematical models; Mathematics; Mathematics and Statistics; Minima; Operations Research/Decision Theory; Optimization; Real Functions; Studies; Variables; 91A10; Optimization reformulations; 90C30; Regularized indicator Nikaidô–Isoda function; Normalized Nash equilibria; Quasi-variational inequality problem; Generalized Nash equilibrium problem
• ISSN: 0925-5001; 1573-2916
• DOI: 10.1007/s10898-012-9978-0

In this paper, we extend the literature by adapting the Nikaidô–Isoda function as an indicator function termed as regularized indicator Nikaidô–Isoda function, and this is demonstrated to guarantee existence of a solution. Using this function, we present two constrained optimization reformulations of the generalized Nash equilibrium problem (GNEP for short). The first reformulation characterizes all the solutions of GNEP as global minima of the optimization problem. Later this approach is modified to obtain the second optimization reformulation whose global minima characterize the normalized Nash equilibria. Some numerical results are also included to illustrate the behaviour of the optimization reformulations.