Open Access
2008 On Gap Functions for Quasi-Variational Inequalities
Kouichi Taji
Abstr. Appl. Anal. 2008: 1-7 (2008). DOI: 10.1155/2008/531361


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.


Download Citation

Kouichi Taji. "On Gap Functions for Quasi-Variational Inequalities." Abstr. Appl. Anal. 2008 1 - 7, 2008.


Published: 2008
First available in Project Euclid: 9 September 2008

zbMATH: 1357.49046
MathSciNet: MR2393109
Digital Object Identifier: 10.1155/2008/531361

Rights: Copyright © 2008 Hindawi

Vol.2008 • 2008
Back to Top