Parallel implementation of augmented Lagrangian method within L-shaped method for stochastic linear programs

Abstract

In this paper, we study two-stage stochastic linear programming (SLP) problems with fixed recourse. The problem is often large scale as the objective function involves an expectation over a discrete set of scenarios. This paper presents a parallel implementation of the augmented Lagrangian method for solving SLPs. Our parallel method is based on a modified version of the L-shaped method and reducing linear master and recourse programs to unconstrained maximization of concave differentiable piecewise quadratic functions. The maximization problem is solved using the generalized Newton method. The parallel method is implemented in MATLAB. Large scale SLP with several millions of variables and several hundreds of thousands of constraints are solved. The results of uniprocessor and multiprocessor computations are presented which show that the parallel algorithm is effective.