Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/17904
Title: Gap functions and existence of solutions to set-valued vector variational inequalities
Authors: Yang, XQ 
Yao, JC
Keywords: existence of a solution
gap functions
semi-infinite programming
set-valued mappings
Vector variational inequalities
Issue Date: 2002
Publisher: Springer
Source: Journal of optimization theory and applications, 2002, v. 115, no. 2, p. 407-417 How to cite?
Journal: Journal of optimization theory and applications 
Abstract: The variational inequality problem with set-valued mappings is very useful in economics and nonsmooth optimization. In this paper, we study the existence of solutions and the formulation of solution methods for vector variational inequalities (VVI) with set-valued mappings. We introduce gap functions and establish necessary and sufficient conditions for the existence of a solution of the VVI. It is shown that the optimization problem formulated by using gap functions can be transformed into a semi-infinite programming problem. We investigate also the existence of a solution for the generalized VVI with a set-valued mapping by virtue of the existence of a solution of the VVI with a single-valued function and a continuous selection theorem.
URI: http://hdl.handle.net/10397/17904
ISSN: 0022-3239
EISSN: 1573-2878
DOI: 10.1023/A:1020844423345
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