# Convergence rate of a proximal multiplier algorithm for separable convex minimization

The proximal multiplier method with proximal distances (PMAPD) proposed by O. Sarmiento C., E. A. Papa Quiroz and P. R. Oliveira, applied to solve a convex program with separable structure unified the works of Chen and Teboulle (PCPM method), Kyono and Fukushima (NPCPMM) and Auslender and Teboulle (EPDM) and extended the convergence properties for the class of $\varphi-$divergence distances. In this paper, we show that under standard assumptions the iterations generated by the (PMAPD) converge linearly to the unique optimal solution of the problem.

## Citation

Report2-PRO, PESC-COPPE-UFRJ