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Expected Utility, Penalty Functions, and Duality in Stochastic Nonlinear Programming

Author

Listed:
  • Aharon Ben-Tal

    (Technion---Israel Institute of Technology, Haifa, Israel)

  • Marc Teboulle

    (Dalhousie University, Halifax, Nova Scotia, Canada)

Abstract

We consider nonlinear programming problem (P) with stochastic constraints. The Lagrangean corresponding to such problems has a stochastic part, which in this work is replaced by its certainty equivalent (in the sense of expected utility theory). It is shown that the deterministic surrogate problem (CE-P) thus obtained, contains a penalty function which penalizes violation of the constraints in the mean. The approach is related to several known methods in stochastic programming such as: chance constraints, stochastic goal programming, reliability programming and mean-variance analysis. The dual problem of (CE-P) is studied (for problems with stochastic righthand sides in the constraints) and a comprehensive duality theory is developed by introducing a new certainty equivalent (NCE) concept. Motivation for the NCE and its potential role in Decision Theory are discussed, as well as mean-variance approximations.

Suggested Citation

  • Aharon Ben-Tal & Marc Teboulle, 1986. "Expected Utility, Penalty Functions, and Duality in Stochastic Nonlinear Programming," Management Science, INFORMS, vol. 32(11), pages 1445-1466, November.
    • Handle: RePEc:inm:ormnsc:v:32:y:1986:i:11:p:1445-1466
    DOI: 10.1287/mnsc.32.11.1445
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