关键词: sparable convex optimization, convex combination proximal centers, relative error criterion, ISPADMM, ergodic sublinear convergence rate

Abstract: In this paper, we develop an inexact symmetric proximal alternating direction method of multipliers (ISPADMM) with two convex combinations (ISPADMM-tcc) for solving two-block separable convex optimization problems with linear equality constraints. Specifically, the convex combination technique is incorporated into the proximal centers of both subproblems. We then approximately solve these two subproblems based on relative error criteria. The global convergence, and $O(\frac{1}{N})$ ergodic sublinear convergence rate measured by the function value residual and constraint violation are established under some mild conditions, where $N$ denotes the number of iterations. Finally, numerical experiments on solving the $l_1$-regularized analysis sparse recovery and the elastic net regularization regression problems illustrate the feasibility and effectiveness of the proposed method.

Key words: sparable convex optimization, convex combination proximal centers, relative error criterion, ISPADMM, ergodic sublinear convergence rate