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Gap Function for Set-Valued Vector Variational-Like Inequalities.
- Source :
- Journal of Optimization Theory & Applications; Jul2008, Vol. 138 Issue 1, p77-84, 8p
- Publication Year :
- 2008
-
Abstract
- Variational-like inequalities with set-valued mappings are very useful in economics and nonsmooth optimization problems. In this paper, we study the existence of solutions and the formulation of solution methods for vector variational-like inequalities (VVLI) with set-valued mappings. We introduce gap functions and establish necessary and sufficient conditions for the existence of a solution of the VVLI. We investigate the existence of a solution for the generalized VVLI with a set-valued mapping by exploiting the existence of a solution of the VVLI with a single-valued function and a continuous selection theorem. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00223239
- Volume :
- 138
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Journal of Optimization Theory & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 32919507
- Full Text :
- https://doi.org/10.1007/s10957-008-9401-7