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

Abstract

This document considers nonlinear programming problems with stochastic constraints. The Lagrangian 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 thus obtained, contains a penalty function which penalized violation of the constraints in the mean. The dual problem is studied (for problems with stochastic righthand sides in the constraints) and a comprehensive duality theory is developed by introducing a new certainty equivalent concept, which possesses, for arbitrary utility functions, some of the properties that the classical certainty equivalent retains only for the exponential utility. Additional keywords: Minmax theorems; Convex functions; and Risk aversion. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1985
Accession Number
ADA154034

Entities

People

  • A. Ben-tal
  • Marc Teboulle

Organizations

  • University of Texas at Austin

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  • Abstracts
  • Applied Mathematics
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  • Computer Programming
  • Economic Analysis
  • Inequalities
  • Linear Programming
  • Mathematical Programming
  • Nonlinear Programming
  • Optimization
  • Probability
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  • Mathematics

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