Sensitivity analysis of optimal solutions for objective functions with stochastic parameters.

Abstract

The purpose of this paper is to develop a definitional framework for the constrained optimization of an objective function with stochastic parameters. Included in this definitional framework are the construction of a deterministic reformulation for the stochastic problem, guidelines for selecting an algorithm for optimizing the deterministic reformulation and a criterion, called invariance, which is used for solution sensitivity analysis in the context of stochastic parameter behavior. Illustration of the application of the definitional framework and an analysis of the conditions imposed by the invariance criterion is provided for linear, piecewise linear, and quadratic functions.