Programming Under Uncertainty: The Solution Set

Abstract

In a previous paper [8], we described and characterized the equivalent convex program of a two-stage linear program under uncertainty. We proved that the solution set of a linear program under uncertainty is convex and derived explicit expressions for this set for some particular cases. The main result of this paper is to show that the solution set is not only convex but also polyhedral. It is also shown that the equivalent convex program of a multi-stage programming under uncertainty problem is of the form: Minimize a convex function subject to linear constraints.

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