Merit functions and error bounds for constrained mixed set-valued variational inequalities via generalized f-projection operators. (2nd August 2016)

• Record Type: Journal Article
• Authors: Li, Chuqun; Li, Jun
• Is Part Of: Optimization. Volume 65:Number 8(2016)
• Page Start: 1569
• Page End: 1584
• Publication Date: 2016-08-02
• Subjects: Convex programming -- mixed set-valued variational inequality -- generalized f-projection operator -- merit functions -- error bounds; 90C25 -- 90C30; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1163555
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we introduce and investigate a constrained mixed set-valued variational inequality (MSVI) in Hilbert spaces. We prove the solution set of the constrained MSVI is a singleton under strict monotonicity. We also propose four merit functions for the constrained MSVI, that is, the natural residual, gap function, regularized gap function and D-gap function. We further use these functions to obtain error bounds, i.e. upper estimates for the distance to solutions of the constrained MSVI under strong monotonicity and Lipschitz continuity. The approach exploited in this paper is based on the generalized f -projection operator due to Wu and Huang, but not the well-known proximal mapping.