On proximal augmented Lagrangian based decomposition methods for dual block-angular convex composite programming problems

We design inexact proximal augmented Lagrangian based decomposition methods for convex composite programming problems with dual block-angular structures. Our are particularly well suited quadratic arising from stochastic models. The algorithmic framework is on the application of abstract ADMM developed in [Chen, Sun, Toh, Math. Prog. 161:237–270] to target problem, as recently symmetric Gauss-Seidel theorem solving a multi-block problem. key issues our firstly designing appropriate terms decompose computation variable blocks problem make subproblems each iteration easier solve, and secondly develop novel numerical schemes solve decomposed efficiently. have guaranteed convergence. present an proposed algorithms doubly nonnegative relaxations uncapacitated facility location problems, two-stage optimization problems. conduct numerous experiments evaluate performance method against state-of-the-art solvers such Gurobi MOSEK. Moreover, also compare favourably well-known progressive hedging algorithm Rockafellar Wets.