Strict Feasibility for Generalized Mixed Variational Inequality in Reflexive Banach Spaces

Strict Feasibility for Generalized Mixed Variational Inequality in Reflexive Banach Spaces

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Article ID: iaor2012617
Volume: 152
Issue: 3
Start Page Number: 696
End Page Number: 709
Publication Date: Mar 2012
Journal: Journal of Optimization Theory and Applications
Authors: ,
Keywords: Banach space
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.

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