Partial proximal method of multipliers for convex programming problems

Two variants of the partial proximal method of multipliers are proposed for solving convex programming problems with linear constraints, where the objective function is expressed as the sum of two convex functions. The iteration of each algorithm consists of computing an approximate saddle point of the augmented Lagrangian. The global convergence is established under an approximation cirterion for computing the saddle point. In particular, for the convex programming problem with multiple set constraints and the traffic assignment problem, one of the proposed algorithms can effectively be implemented on a parallel computer.