A proximal multiplier method for separable convex minimization. (1st February 2016)

• Record Type: Journal Article
• Authors: Sarmiento, O.; Papa Quiroz, E.A.; Oliveira, P.R.
• Is Part Of: Optimization. Volume 65:Number 2(2016)
• Page Start: 501
• Page End: 537
• Publication Date: 2016-02-01
• Subjects: proximal multiplier methods -- separable convex problems -- proximal distances -- convex functions; 52A41; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2015.1062009
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we propose an inexact proximal multiplier method using proximal distances for solving convex minimization problems with a separable structure. The proposed method unifies the works of Chen and Teboulle (PCPM method), Kyono and Fukushima (NPCPMM) and Auslender and Teboulle (EPDM), and extends the convergence properties for the class of -divergence distances. We prove, under standard assumptions, that the iterations generated by the method are well defined and the sequence converges to an optimal solution of the problem.