Gap Function for Set-Valued Vector Variational-Like Inequalities

S. K. Mishra (), S. Y. Wang and K. K. Lai
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S. K. Mishra: G.B. Pant University of Agriculture and Technology
S. Y. Wang: Chinese Academy of Sciences
K. K. Lai: City University of Hong Kong

Journal of Optimization Theory and Applications, 2008, vol. 138, issue 1, No 6, 77-84

Abstract: 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.

Keywords: Vector variational-like inequalities; Set-valued mappings; Gap functions; Existence of a solution; Semidefinite programming (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-008-9401-7

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