1. On Gap Functions for Quasi-Variational Inequalities.
- Author
-
Taji, Kouichi
- Subjects
MATHEMATICS ,MATHEMATICAL analysis ,VARIATIONAL inequalities (Mathematics) ,MATHEMATICAL optimization ,FUNCTIONAL analysis ,FUNCTIONALS - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2008
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