An Algorithm for the Minimum-Risk Problem of Stochastic Programming

Abstract

This paper presents a computational procedure for the solution—via reduction to a parametric quadratic program—of the “minimum-risk problem” associated with a stochastic linear program where costs are random variables with normal multidimensional joint distribution, i.e., for the nonlinear program max x ϵ X ( c ′ x − t )/( x ′ Vx ) 1/2 in where t is a given number, V a positive-definite matrix, and X a given convex polyhedron in n -dimensional Euclidean space R n .