positive-indefinite proximal regularization

On the Optimal Proximal Parameter of an ADMM-like Splitting Method for Separable Convex Programming

Published: 2017/10/01

Convex Optimization convergence analysis, convex optimization, positive-indefinite proximal regularization, splitting method

An ADMM-based splitting method is proposed in [11] for solving convex minimization problems with linear constraints and multi-block separable objective functions; while a relatively large proximal parameter is required for theoretically ensuring the convergence. In this paper, we further study this method and find its optimal (smallest) proximal parameter. For succinctness, we focus on the … Read more

Improving an ADMM-like Splitting Method via Positive-Indefinite Proximal Regularization for Three-Block Separable Convex Minimization

Published: 2016/08/13

Bingsheng He

Xiao-Ming Yuan

Convex Optimization alternating direction method of multipliers, augmented lagrangian method, convergence analysis, convex optimization, positive-indefinite proximal regularization, three-block

The augmented Lagrangian method (ALM) is fundamental for solving convex minimization models with linear constraints. When the objective function is separable such that it can be represented as the sum of more than one function without coupled variables, various splitting versions of the ALM have been well studied in the literature such as the alternating … Read more