A NEW ACCELERATED POSITIVE-INDEFINITE PROXIMAL ADMM FOR CONSTRAINED SEPARABLE CONVEX OPTIMIZATION PROBLEMS

The alternating direction method of multipliers (ADMM) is a powerful method to solve con-strained convex optimization problems with the separable structure. The ADMM with the positive -indefinite proximal terms, which has ergodic convergent rate O( K1 ) with the number of iterations K, is more general than the ADMM with positive-definite proximal terms. In this paper, we propose a new accelerated positive-indefinite proximal linearized ADMM algorithm with positive-indefinite proximal matrix by the techniques of extrapolation. We obtain the nonergodic convergence rate O( K1 ) in the sense of objective values and the nonergodic convergence rate O(1 root K) in the sense of iterative sequence of the proposed method as well as the upper bound of the violation of constraints. Numerical results are reported to show the efficiency of the proposed method.