Weakly sharp solutions and finite convergence of algorithms for a variational inequality problem. (1st February 2018)

• Record Type: Journal Article
• Authors: Liu, Yina
• Is Part Of: Optimization. Volume 67:Number 2(2018)
• Page Start: 329
• Page End: 340
• Publication Date: 2018-02-01
• Subjects: Variational inequality -- gap functions -- gâteaux differentiable -- locally Lipschitz property -- weakly sharp solution -- error bound -- convergence of an algorithm; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1397146
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: The aim of the paper is to characterize weakly sharp solutions of a variational inequality problem. In particular, we present weak sharpness results by using primal and dual gap functions, g and G, and also without considering gap functions, either. The subdifferential and locally Lipschitz properties of for are first studied since they are useful for discussing weakly sharp solutions of the variational inequality. A result of finite termination of a class of algorithms for solving the variational inequality problem is also studied.