Accession Number:

ADA513135

Title:

Optimality Functions in Stochastic Programming

Descriptive Note:

Corporate Author:

NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF OPERATIONS RESEARCH

Personal Author(s):

Report Date:

2009-12-02

Pagination or Media Count:

31.0

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.

Subject Categories:

  • Statistics and Probability
  • Operations Research

Distribution Statement:

APPROVED FOR PUBLIC RELEASE