# American Institute of Mathematical Sciences

April  2007, 3(2): 165-171. doi: 10.3934/jimo.2007.3.165

## A class of gap functions for quasi-variational inequality problems

 1 Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501

Received  August 2006 Revised  October 2006 Published  April 2007

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.
Citation: Masao Fukushima. A class of gap functions for quasi-variational inequality problems. Journal of Industrial & Management Optimization, 2007, 3 (2) : 165-171. doi: 10.3934/jimo.2007.3.165
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