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On relations between chance constrained and penalty function problems under discrete distributions. (English) Zbl 1284.90044

The author extends the theory of penalty functions to stochastic programming problems with nonlinear inequality constraints dependent on a random vector with a known distribution. Firstly, he proposes the formulations of the chance constrained and penalty function problems and derives the asymptotic equivalence of the two problems under finite discrete distributions with general known probabilities. Bounds on optimal values and the convergence of the optimal solutions are proposed. Finally, the author applies exact penalization under a modified calmness property in order to improve the results.

MSC:

90C15 Stochastic programming
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