SOLVING CHANCE-CONSTRAINED PROBLEMS VIA A SMOOTH SAMPLE-BASED NONLINEAR APPROXIMATION

作     者：Pena-Ordieres, Alejandra Luedtke, James R. Wachter, Andreas 

作者机构：Northwestern Univ Dept Ind Engn & Management Sci Evanston IL 60208 USA Univ Wisconsin Dept Ind & Syst Engn Madison WI 53706 USA 

出 版 物：《SIAM JOURNAL ON OPTIMIZATION》 (工业与应用数学会最优化杂志)

年 卷 期：2020年第30卷第3期

页      面：2221-2250页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：National Science Foundation [DMS-1522747] U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research (ASCR) [DE-AC02-06CH11357] Los Alamos National Laboratory Center for Nonlinear Studies Ulam Fellows program National Nuclear Security Administration of U.S. Department of Energy [89233218CNA000001] NNSA of the U.S. DOE at LANL [DE-AC52-06NA25396] 

主　　题：chance constraints nonlinear optimization quantile function sample average approximation smoothing sequential quadratic programming trust region 

摘      要：We introduce a new method for solving nonlinear continuous optimization problems with chance constraints. Our method is based on a reformulation of the probabilistic constraint as a quantile function. The quantile function is approximated via a differentiable sample average approximation. We provide theoretical statistical guarantees of the approximation and illustrate empirically that the reformulation can be directly used by standard nonlinear optimization solvers in the case of single chance constraints. Furthermore, we propose an SeiQP-type trust -region method to solve instances with joint chance constraints. We demonstrate the performance of the method on several problems and show that it scales well with the sample size and that the smoothing can be used to counteract the bias in the chance constraint approximation induced by the sample approximation.