Positive-Indefinite Proximal Augmented Lagrangian Method and its Application to Full Jacobian Splitting for Multi-block Separable Convex Minimization Problems

The augmented Lagrangian method (ALM) is fundamental for solving convex programming problems with linear constraints. The proximal version of ALM, which regularizes ALM’s subproblem over the primal variable at each iteration by an additional positive-definite quadratic proximal term, has been well studied in the literature. In this paper, we show that it is not necessary … Read more