Approximate proximal algorithms for generalized variational inequalities with pseudomonotone multifunctions

✍ Scribed by Ceng, L. C. (author);Yao, J. C. (author)

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 216 KB
• Volume: 213
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2007.01.034

✦ Synopsis

The purpose of this paper is to investigate the convergence of general approximate proximal algorithm (resp. general Bregmanfunction-based approximate proximal algorithm) for solving the generalized variational inequality problem (for short, GVI(T , ) where T is a multifunction). The general approximate proximal algorithm (resp. general Bregman-function-based approximate proximal algorithm) is to define new approximating subproblems on the domains n ⊃ , n = 1, 2, . . . , which form a general approximate proximate point scheme (resp. a general Bregman-function-based approximate proximate point scheme) for solving GVI(T , ). It is shown that if T is either relaxed -pseudomonotone or pseudomonotone, then the general approximate proximal point scheme (resp. general Bregman-function-based approximate proximal point scheme) generates a sequence which converges weakly to a solution of GVI(T , ) under quite mild conditions.