Optimal Linearized Alternating Direction Method of Multipliers for Convex Programming

The alternating direction method of multipliers (ADMM) is being widely used in a variety of areas; its different variants tailored for different application scenarios have also been deeply researched in the literature. Among them, the linearized ADMM has received particularly wide attention from many areas because of its efficiency and easy implementation. To theoretically guarantee … Read more

Convergence Study on the Proximal Alternating Direction Method with Larger Step Size

The alternating direction method of multipliers (ADMM) is a popular method for the separable convex programming with linear constraints, and the proximal ADMM is its important variant. Previous studies show that the relaxation factor $\gamma\in (0, \frac{1+\sqrt{5}}{2})$ by Fortin and Glowinski for the ADMM is also valid for the proximal ADMM. In this paper, we … Read more


We consider a regularization proximal method with variable metric to solve the nonlinear complementarity problem (NCP) for P0-functions. We establish global convergence properties when the solution set is non empty and bounded. Furthermore, we prove, without boundedness of the solution set, that the sequence generated by the algorithm is a minimizing sequence for the implicit … Read more

A new class of proximal algorithms for the nonlinear complementarity problem

In this paper, we consider a variable proximal regularization method for solving the nonlinear complementarity problem for P0 functions. Citation Applied Optimization Series, 96, Optimization and Control With Applications, L. Qi, K. Teo and X. Yang (Eds.), pp 549-561, Springer, 2005.