Abstract and Applied Analysis

On Gap Functions for Quasi-Variational Inequalities

Kouichi Taji

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2008 (2008), Article ID 531361, 7 pages.

Dates
First available in Project Euclid: 9 September 2008

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1220969144

Digital Object Identifier
doi:10.1155/2008/531361

Mathematical Reviews number (MathSciNet)
MR2393109

Zentralblatt MATH identifier
1357.49046

Citation

Taji, Kouichi. On Gap Functions for Quasi-Variational Inequalities. Abstr. Appl. Anal. 2008 (2008), Article ID 531361, 7 pages. doi:10.1155/2008/531361. https://projecteuclid.org/euclid.aaa/1220969144


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