Gap Function for Set-Valued Vector Variational-Like Inequalities
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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.
KeywordsVector variational-like inequalities Set-valued mappings Gap functions Existence of a solution Semidefinite programming
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