A partial inexact proximal point method for separable convex programming

Abstract:

In this paper, a new method is proposed for solving a class of separable convex programming problem. The method is referred to as the partial inexact proximal point method. In the method, we take a fresh look at the alternating direction method of multipliers and two sub-problems are solved independently. One is solved directly and the other is handled by bring in inexact minimization. Convergence of the method is proved under mild assumptions and its efficiency is also verified by numerical experiments.