Mathematical Methods of Operations Research

, Volume 77, Issue 2, pp 265–277 | Cite as

On relations between chance constrained and penalty function problems under discrete distributions

Original Article

Abstract

We extend the theory of penalty functions to stochastic programming problems with nonlinear inequality constraints dependent on a random vector with known distribution. We show that the problems with penalty objective, penalty constraints and chance constraints are asymptotically equivalent under discretely distributed random parts. This is a complementary result to Branda (Kybernetika 48(1):105–122, 2012a), Branda and Dupačová (Ann Oper Res 193(1):3–19, 2012), and Ermoliev et al. (Ann Oper Res 99:207–225, 2000) where the theorems were restricted to continuous distributions only. We propose bounds on optimal values and convergence of optimal solutions. Moreover, we apply exact penalization under modified calmness property to improve the results.

Keywords

Penalty functions Chance constraints Asymptotic equivalence Discrete distribution Exact penalization Calmness 

Mathematics Subject Classification (2000)

90C15 

Notes

Acknowledgments

The research was supported by the Czech Science Foundation under the Grant (P402/12/G097).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Probability and Mathematical Statistics, Faculty of Mathematics and PhysicsCharles University in PraguePragueCzech Republic

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