Journal of Industrial and Management Optimization (JIMO)

A class of gap functions for quasi-variational inequality problems

Pages: 165 - 171, Volume 3, Issue 2, May 2007      doi:10.3934/jimo.2007.3.165

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Masao Fukushima - Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan (email)

Abstract: We present a class of gap functions for the quasi-variational inequality problem (QVIP). We show the equivalence between the optimization reformulation with the gap function and the original QVIP. We also give conditions under which the gap function is continuous and directionally differentiable.

Keywords:  Quasi-variational inequality problem, optimization reformulation, gap function.
Mathematics Subject Classification:  Primary: 65K10; Secondary: 90C30.

Received: August 2006;      Revised: October 2006;      Available Online: April 2007.