Stochastic Optimization Problems with Incomplete Information on Distribution Functions

Abstract

The main purpose of this paper is to discuss numerical optimization procedures, based on duality theory, for stochastic extremal problems in which the distribution function is only partially known. We formulate such problems as minimax problems in which the “inner” problem involves optimization with respect to probability measures. The latter problem is solved using generalized linear programming techniques. Then we state the dual problem to the initial stochastic optimization problem. Numerical procedures that avoid the difficulties associated with solving the “inner” problem are proposed.