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

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 o...

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Published inJournal of global optimization Vol. 57; no. 3; pp. 843 - 861
Main Authors Lalitha, C. S., Dhingra, Mansi
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.11.2013
Springer
Springer Nature B.V
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ISSN0925-5001
1573-2916
DOI10.1007/s10898-012-9978-0

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Summary: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.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-012-9978-0