An LQP-Based Symmetric Alternating Direction Method of Multipliers with Larger Step Sizes

Abstract

Symmetric alternating direction method of multipliers (ADMM) is an efficient method for solving a class of separable convex optimization problems. This method updates the Lagrange multiplier twice with appropriate step sizes at each iteration. However, such step sizes were conservatively shrunk to guarantee the convergence in recent studies. In this paper, we are devoted to seeking larger step sizes whenever possible. The logarithmic-quadratic proximal (LQP) terms are applied to regularize the symmetric ADMM subproblems, allowing the constrained subproblems to then be converted to easier unconstrained ones. Theoretically, we prove the global convergence of such LQP-based symmetric ADMM by specifying a larger step size domain. Moreover, the numerical results on a traffic equilibrium problem are reported to demonstrate the advantage of the method with larger step sizes.