Proximal ADMM with larger step size for two-block separable convex programming and its application to the correlation matrices calibrating problems

The alternating direction method of multipliers (ADMM) is a benchmark for solving two-block separable convex program-ming. However, as other first-order iteration methods, the ADMM also suffers from low convergence. In this paper, to accelerate the convergence of the ADMM, the restriction region of the Fortin and Glowinski’s constant γ in the ADMM is relaxed from (0, 1+ √5 / 2 ) to (0, +∞), thus we get a proximal ADMM with larger step size. By proving some properties of the method, we show its global convergence under mild conditions. Finally, some numerical experiments on the correlation matrices calibrating problems are given to demonstrate the efficiency and the performance of the new method.