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 (Formula presented.) -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.
Bibliographical noteFunding Information:
The research of the first and second authors was supported by CAPES (Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior) and the PosDoctoral Scolarchip CAPES-FAPERJ Edital PAPD-2011, respectively.
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- convex functions
- proximal distances
- proximal multiplier methods
- separable convex problems