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

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  • Martin Branda

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. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Martin Branda, 2013. "On relations between chance constrained and penalty function problems under discrete distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(2), pages 265-277, April.
    • Handle: RePEc:spr:mathme:v:77:y:2013:i:2:p:265-277
    DOI: 10.1007/s00186-013-0428-7
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    References listed on IDEAS

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    7. Y.M. Ermoliev & T.Y. Ermolieva & G.J. MacDonald & V.I. Norkin, 2000. "Stochastic Optimization of Insurance Portfolios for Managing Exposure to Catastrophic Risks," Annals of Operations Research, Springer, vol. 99(1), pages 207-225, December.
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