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.‎