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.
Serial and Parallel Solution of Large Scale Linear Programs by Augmented Lagrangian Successive Overrelaxation