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

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.

• 저널Management Science · 32(11) · 1445–1466
• 토픽Optimization and Mathematical Programming · Control and Systems Engineering
• DOI10.1287/mnsc.32.11.1445
• 저자Aharon Ben‐Tal, Marc Teboulle