Optimality Functions in Stochastic Programming

Abstract

Optimality functions in nonlinear programming conveniently measure, in some sense, the distance between a candidate solution and a stationary point. They may also provide guidance towards the development of implementable algorithms. In this paper, we use an optimality function to construct procedures for validation analysis in stochastic programs with nonlinear, possibly nonconvex, expected value functions as both objective and constraint functions. We construct an estimator of the optimality function and examine its consistency, bias, and asymptotic distribution. The estimator leads to confidence intervals for the value of the optimality function at a candidate solution and, hence, provides a quantitative measure of solution quality. We also construct an implementable algorithm for solving smooth stochastic programs based on sample average approximations and the optimality function estimator. Preliminary numerical tests illustrate the proposed algorithm and validation analysis procedures.

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Document Details

Document Type
Technical Report
Publication Date
Dec 02, 2009
Accession Number
ADA513135

Entities

People

  • J. O. Royset

Organizations

  • Naval Postgraduate School

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Computational Science
  • Computer Programming
  • Computers
  • Convergence
  • Directional
  • Distribution Functions
  • Engineering
  • Estimators
  • Inequalities
  • Inventory Control
  • Nonlinear Programming
  • Operations Research
  • Optimization
  • Probability
  • Random Variables
  • Validation

Fields of Study

  • Mathematics

Readers

  • Operations Research
  • Statistical inference.