Adaptive subgradient method for the split quasi-convex feasibility problems. (2nd October 2016)

• Record Type: Journal Article
• Authors: Nimana, Nimit; Farajzadeh, Ali P.; Petrot, Narin
• Is Part Of: Optimization. Volume 65:Number 10(2016)
• Page Start: 1885
• Page End: 1898
• Publication Date: 2016-10-02
• Subjects: Split feasibility problem -- quasi-convex feasibility problem -- adaptive subgradient method -- convergence; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1189551
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we consider a type of the celebrated convex feasibility problem, named as split quasi-convex feasibility problem (SQFP). The SQFP is to find a point in a sublevel set of a quasi-convex function in one space and its image under a bounded linear operator is contained in a sublevel set of another quasi-convex function in the image space. We propose a new adaptive subgradient algorithm for solving SQFP problem. We also discuss the convergence analyses for two cases: the first case where the functions are upper semicontinuous in the setting of finite dimensional, and the second case where the functions are weakly continuous in the infinite-dimensional settings. Finally some numerical examples in order to support the convergence results are given.