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

Aharon Ben-Tal and Marc Teboulle
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Aharon Ben-Tal: Technion---Israel Institute of Technology, Haifa, Israel
Marc Teboulle: Dalhousie University, Halifax, Nova Scotia, Canada

Management Science, 1986, vol. 32, issue 11, 1445-1466

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.

Keywords: stochastic programming; duality; minmax theorems; expected utility; mean-variance (search for similar items in EconPapers)
Date: 1986
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