A MAJORIZED ADMM WITH INDEFINITE PROXIMAL TERMS FOR LINEARLY CONSTRAINED CONVEX COMPOSITE OPTIMIZATION

This paper presents a majorized alternating direction method of multipliers (ADMM) with indefinite proximal terms for solving linearly constrained 2-block convex composite optimization problems with each block in the objective being the sum of a nonsmooth convex function (p(x) or q(y)) and a smooth convex function (f(x) or g(y)), i.e., min(x is an element of X, y is an element of Y) {p(x) + f(x) + q(y) + g(y) vertical bar A*x + B*y - c}. By choosing the indefinite proximal terms properly, we establish the global convergence and the iteration-complexity in the nonergodic sense of the proposed method for the step-length tau is an element of(0, (1 + root 5)/2). The computational benefit of using indefinite proximal terms within the ADMM framework instead of the current requirement of positive semidefinite ones is also demonstrated numerically. This opens up a new way to improve the practical performance of the ADMM and related methods.