Gap Function for Set-Valued Vector Variational-Like Inequalities |
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| Authors: | S K Mishra S Y Wang K K Lai |
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| Institution: | (1) Department of Mathematics and Statistics, College of Basic Sciences and Humanities, G.B. Pant University of Agriculture and Technology, Pantnagar, 263145, India;(2) City University of Hong Kong, Department of Management Sciences, 83 Tat Chee Avenue, Kowloon, Hong Kong;(3) Present address: Department of Mathematics, Banaras Hindu University, Varanasi, 221005, India;(4) Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, China |
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| 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.
The research of first author was partially supported by the Council of Scientific and Industrial Research, New Delhi, Ministry
of Human Resources Development, Government of India Grant 25(0132)/ER-II/2004. |
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| Keywords: | Vector variational-like inequalities Set-valued mappings Gap functions Existence of a solution Semidefinite programming |
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