On Gap Functions for Quasi-Variational Inequalities

Kouichi Taji

Abstract and Applied Analysis, 2008, vol. 2008, 1-7

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.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:531361

DOI: 10.1155/2008/531361

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