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- Title
Gap Function for Set-Valued Vector Variational-Like Inequalities.
- Authors
Mishra, S. K.; Wang, S. Y.; Lai, K. K.
- 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.
- Subjects
VARIATIONAL inequalities (Mathematics); MATHEMATICAL optimization; NONSMOOTH optimization; SELECTION theorems; MATHEMATICAL mappings; SET-valued maps; MATHEMATICAL analysis; MATHEMATICAL programming; SET theory; TOPOLOGICAL spaces
- Publication
Journal of Optimization Theory & Applications, 2008, Vol 138, Issue 1, p77
- ISSN
0022-3239
- Publication type
Article
- DOI
10.1007/s10957-008-9401-7