Strict Feasibility for Generalized Mixed Variational Inequality in Reflexive Banach Spaces

Ren-you Zhong and Nan-jing Huang ()
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Ren-you Zhong: Sichuan University
Nan-jing Huang: Sichuan University

Journal of Optimization Theory and Applications, 2012, vol. 152, issue 3, No 8, 696-709

Abstract: Abstract The purpose of this paper is to investigate the nonemptiness and boundedness of solution set for a generalized mixed variational inequality with strict feasibility in reflexive Banach spaces. A concept of strict feasibility for the generalized mixed variational inequality is introduced, which recovers the existing concepts of strict feasibility for variational inequalities and complementarity problems. By using the equivalence characterization of nonemptiness and boundedness of the solution set for the generalized mixed variational inequality due to Zhong and Huang (J. Optim. Theory Appl. 147:454–472, 2010), it is proved that the generalized mixed variational inequality problem has a nonempty bounded solution set is equivalent to its strict feasibility.

Keywords: Banach Space; Variational Inequality; Convex Subset; Optim Theory; Equilibrium Problem (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-011-9914-3

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