Optimality functions in stochastic programming

• 成果类型: Article
• 署名作者: Royset, J. O.
• 署名单位: United States Department of Defense; United States Navy; Naval Postgraduate School
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-011-0453-3
• 发表日期: 2012
• 页码: 293-321
• 关键词: sample average approximation; Failure probability; optimization; DESIGN

摘要

Optimality functions define stationarity in nonlinear programming, semi-infinite optimization, and optimal control in some sense. In this paper, we consider optimality functions for stochastic programs with nonlinear, possibly nonconvex, expected value objective and constraint functions. We show that an optimality function directly relates to the difference in function values at a candidate point and a local minimizer. We construct confidence intervals for the value of the optimality function at a candidate point and, hence, provide a quantitative measure of solution quality. Based on sample average approximations, we develop an algorithm for classes of stochastic programs that include CVaR-problems and utilize optimality functions to select sample sizes.