A Regularized Algorithm for Solving Two-Stage Stochastic Linear Programming Problems: A Water Resources Example

Abstract

Stochastic linear programming problems are linear programming problems in which one or more data elements are random variables. Two-stage stochastic linear programming problems are problems in which a first stage decision is made before the random variables are observed. A second stage, or recourse decision, which varies with these observations, compensates for any deficiencies that result from the earlier decision. In this paper, an algorithm for solving stochastic linear programming problems with recourse is presented. Referred to as Regularized Stochastic Decomposition, the algorithm is a major improvement over the original Stochastic Decomposition algorithm. It was developed to be computationally more efficient than the original by introducing a quadratic proximal term in the master program objective function and altering the manner in which the recourse function approximations are updated. The addition of the quadratic regularizing term in the master program objective function justifies a cut dropping scheme that allows one to bound the size of the master programs. The algorithm is applied to a water resources problem assuming continuous random variables.