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**Designing approximation schemes for stochastic optimization problems, in particular for stochastic programs with recourse.**
*(English)*
Zbl 0603.90104

The authors deal with the problem of discrete approximation of stochastic programming problems in which the optimum is sought with respect to the mathematical expectation of a random function. Especially, they pay great attention to two-stage stochastic programming problems.

The paper is divided into 7 main parts not counting the introduction and the conclusion. The basic definitions and the properties of two-stage stochastic linear programming problems and epi-convergence are given in the first two parts. Further, the authors present and study some approximations for which they utilize the properties of convex functions, conditional probabilities, extremal probability measures, moment problems, majority probability measures etc. They obtain some upper and lower bounds for the optimal value. Moreover, they proved some limit theorems. They apply the general results to the special cases of two- stage stochastic linear programming problems.

The paper is written in a very understandable way and it gives a survey on this topic.

The paper is divided into 7 main parts not counting the introduction and the conclusion. The basic definitions and the properties of two-stage stochastic linear programming problems and epi-convergence are given in the first two parts. Further, the authors present and study some approximations for which they utilize the properties of convex functions, conditional probabilities, extremal probability measures, moment problems, majority probability measures etc. They obtain some upper and lower bounds for the optimal value. Moreover, they proved some limit theorems. They apply the general results to the special cases of two- stage stochastic linear programming problems.

The paper is written in a very understandable way and it gives a survey on this topic.

Reviewer: V.Kankova

### MSC:

90C15 | Stochastic programming |