Characterizations of Levitin–Polyak well-posedness by perturbations for the split variational inequality problem. (1st September 2016)

• Record Type: Journal Article
• Authors: Hu, Rong; Fang, Ya-Ping
• Is Part Of: Optimization. Volume 65:Number 9(2016)
• Page Start: 1717
• Page End: 1732
• Publication Date: 2016-09-01
• Subjects: Split variational inequality problem -- split minimization problem -- Levitin–Polyak well-posendness by perturbations -- nonemptiness and boundedness of the solution set; 49K40 -- 49J40 -- 90C31; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1166500
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : The purpose of this paper is to investigate Levitin–polyak well-posedness by perturbations of the split variational inequality problem in reflexive Banach spaces. Furi-Vignoli-type characterizations are established for the well-posedness. We prove that the weak generalized Levitin–Polyak well-posedness by perturbations is equivalent to the nonemptiness and boundedness of the solution set of the problem. Finally, we discuss the relations between the Levitin–Polyak well-posedness by perturbations of the split variational inequality problem and the Levitin–Polyak well-posedness by perturbations of the split minimization problem when the split variational inequality problem arises from the split minimization problem.