# Scenario Approximation of Robust and Chance-Constrained Programs

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## Abstract

We consider scenario approximation of problems given by the optimization of a function over a constraint that is too difficult to be handled but can be efficiently approximated by a finite collection of constraints corresponding to alternative scenarios. The covered programs include min-max games, and semi-infinite, robust and chance-constrained programming problems. We prove convergence of the solutions of the approximated programs to the given ones, using mainly epigraphical convergence, a kind of variational convergence that has demonstrated to be a valuable tool in optimization problems.

## Keywords

Mathematical programming Epigraphical convergence Scenario approximation Sampling## Notes

### Acknowledgements

We are grateful to Christian Hess and Enrico Miglierina for useful comments and discussions, and to the anonymous referees, the Associate Editor Masao Fukushima and the Editor Franco Giannessi for valuable suggestions that helped improve the article substantially.

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