On Stability in Two-Stage Stochastic Nonlinear Programming

Abstract

Two-stage stochastic programming problems are very often assigned to practical optimization problems with random elements. Especially, these models are employed if the basic solution should be determined without knowing the random parameter realization and if the obtained effect can be corrected by a new optimization problem (called the recourse problem) depending on the random elements realization. It is well-known that then the total problem depends on the random elements only through the corresponding probability measure. Consequently, the probability measure can be treated as a parameter in such problems and it is surely reasonable to study the stability with respect to it. The aim of this paper is to study the stability of two-stage nonlinear programming problem with respect to the distribution function. Of course, the linear case is also included in our consideration.Key wordsTwo-stage stochastic programming problemsstabilitystability regiondistribution functions spaceKolmogorov metricAMS classification90C15