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 unified the work of Chen and Teboulle (PCPM method), Kyono and Fukushima (NPCPMM) and Auslender and Teboulle (EPDM) and extends the convergence properties for a class of phi-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.
Report may/2014, PESC-COPPE, Federal University of Rio de Janeiro.
View A proximal multiplier method for separable convex minimization