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

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• 作者：C. S. Lalitha ; Mansi Dhingra
• 关键词：Generalized Nash equilibrium problem ; Regularized indicator Nikaid?–Isoda function ; Optimization reformulations ; Normalized Nash equilibria ; Quasi ; variational inequality problem ; 90C30 ; 91A10
• 刊名：Journal of Global Optimization
• 出版年：2013
• 出版时间：November 2013
• 年：2013
• 卷：57
• 期：3
• 页码：843-861
• 全文大小：433KB
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• 作者单位：C. S. Lalitha (1)
  Mansi Dhingra (2)
  
  1. Department of Mathematics, University of Delhi South Campus, Benito Jaurez Road, New Delhi, 110021, India
  2. Department of Mathematics, University of Delhi, Delhi, 110007, India
  
• ISSN：1573-2916

文摘

In this paper, we extend the literature by adapting the Nikaid?–Isoda function as an indicator function termed as regularized indicator Nikaid?–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.