On the Proximal Jacobian Decomposition of ALM for Multiple-Block Separable Convex Minimization Problems and Its Relationship to

The augmented Lagrangian method (ALM) is a benchmark for solving convex minimization problems with linear constraints. When the objective function of the model under consideration is representable as the sum of some functions without coupled variables, a Jacobian or Gauss-Seidel decomposition is often implemented to decompose the ALM subproblems so that the functions’ properties could be used more effectively in algorithmic design. The Gauss-Seidel decomposition of ALM has resulted in the very popular alternating direction method of multipliers (ADMM) for two-block separable convex minimization models and recently it was shown in [10] that the Jacobian decomposition of ALM is not necessarily convergent. In this paper, we show that if each subproblem of the Jacobian decomposition of ALM is regularized by a proximal term and the proximal coefficient is sufficiently large, the resulting scheme to be called the proximal Jacobian decomposition of ALM, is convergent. We also show that an ...

• Type: Journal
• Year: 2016
• Where: JSCIC
• Authors: Bingsheng He, Hong-Kun Xu, Xiaoming Yuan
• Keywords: JSCIC 2016