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On Gap Functions for Quasi-Variational Inequalities

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  • Kouichi Taji

Abstract

For variational inequalities, various merit functions, such as the gap function, the regularized gap function, the D-gap function and so on, have been proposed. These functions lead to equivalent optimization formulations and are used to optimization-based methods for solving variational inequalities. In this paper, we extend the regularized gap function and the D-gap functions for a quasi-variational inequality, which is a generalization of the variational inequality and is used to formulate generalized equilibrium problems. These extensions are shown to formulate equivalent optimization problems for quasi-variational inequalities and are shown to be continuous and directionally differentiable.

Suggested Citation

  • Kouichi Taji, 2008. "On Gap Functions for Quasi-Variational Inequalities," Abstract and Applied Analysis, Hindawi, vol. 2008, pages 1-7, February.
    • Handle: RePEc:hin:jnlaaa:531361
    DOI: 10.1155/2008/531361
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