Asymptotic behavior of solutions: An application to stochastic NLP

• 成果类型: Article
• 署名作者: Sur, Arnab; Birge, John R.
• 署名单位: University of Chicago
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-020-01554-6
• 发表日期: 2022
• 页码: 281-306
• 关键词: optimization problems; epi-convergence; statistical estimators; UNIFORM-CONVERGENCE; Consistency; approximation; STABILITY; Recourse

摘要

In this article we study the consistency of optimal and stationary (KKT) points of a stochastic non-linear optimization problem involving expectation functionals, when the underlying probability distribution associated with the random variable is weakly approximated by a sequence of random probability measures. The optimization model includes constraints with expectation functionals those are not captured in direct application of the previous results on optimality conditions exist in the literature. We first study the consistency of stationary points of a general NLP problem with convex and locally Lipschitz data and then apply those results to the stochastic NLP problem and stochastic minimax problem. Moreover, we derive an exponential bound for such approximations using a large deviation principle.