Abstract
In this paper, we study the convex optimization problem with linear constraint, and the objective function is composed of m separable convex functions. Considering the special case where the objective function is composed of two separable convex functions, the auxiliary problem principle (APP) is an effective parallel distributed algorithm for solving the special case. Inspired by the principle of APP, a natural idea to solve separable convex optimization problem with m ≥ 3 is to extend the method of APP, resulting in the APP‐like algorithm. The convergence of the APP‐like algorithm is not clear yet. In this paper, we give a sufficient condition for the convergence of the APP‐like algorithm. Specifically, the APP algorithm is a special case of the APP‐like algorithm when m = 2. However, simulation results show that the convergence efficiency of the APP‐like algorithm is affected by the selection of penalty parameter. Therefore, we propose an improved APP‐like algorithm in this paper. Simulation results show that the improved APP‐like algorithm is robust to the selection of penalty parameter and that the convergence efficiency of the improved APP‐like algorithm is better when compared with the APP‐like algorithm.
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