A GAUSSIAN UPPER BOUND FOR GAUSSIAN MULTISTAGE STOCHASTIC LINEAR-PROGRAMS

This paper deals with two-stage and multi-stage stochastic programs in which the right-hand sides of the constraints are Gaussian random var iables. Such problems are of interest since the use of Gaussian estima tors of random variables is widespread. We introduce algorithms to fin d upper bounds on the optimal value of two-stage and multi-stage stoch astic (minimization) programs with Gaussian right-hand sides. The uppe r bounds are obtained by solving deterministic mathematical programmin g problems with dimensions that do not depend on the sample space size . The algorithm for the two-stage problem involves the solution of a d eterministic linear program and a simple semidefinite program. The alg orithm for the multi-stage problem involves the solution of a quadrati cally constrained convex programming problem. (C) 1997 The Mathematica l Programming Society, Inc.