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EXPECTED UTILITY, PENALTY FUNCTIONS, AND DUALITY IN STOCHASTIC NONLINEAR PROGRAMMING.

Authors :
Ben-Tal, Aharon
Teboulle, Marc
Source :
Management Science; Nov86, Vol. 32 Issue 11, p1445-1466, 22p
Publication Year :
1986

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. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00251909
Volume :
32
Issue :
11
Database :
Complementary Index
Journal :
Management Science
Publication Type :
Academic Journal
Accession number :
7347921
Full Text :
https://doi.org/10.1287/mnsc.32.11.1445