文章基本信息

标题：Concentration of Measure for Chance-Constrained Optimization
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作者：Sadegh Soudjani ; Rupak Majumdar
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2018
卷号：51
期号：16
页码：277-282
DOI：10.1016/j.ifacol.2018.08.047
语种：English
出版社：Elsevier
摘要：AbstractChance-constrained optimization problems optimize a cost function in the presence of probabilistic constraints. They are convex in very special cases and, in practice, they are solved using approximation techniques. In this paper, we study approximation of chance constraints for the class of probability distributions that satisfy a concentration of measure property. We show that using concentration of measure, we can transform chance constraints to constraints on expectations, which can then be solved based on scenario optimization. Our approach depends solely on the concentration of measure property of the uncertainty and does not require the objective or constraint functions to be convex. We also give bounds on the required number of scenarios for achieving a certain confidence. We demonstrate our approach on a non-convex chanced-constrained optimization, and benchmark our technique against alternative approaches in the literature on chance-constrained LQG problem.
关键词：KeywordsChance-Constrained OptimizationNon-Convex Scenario ProgramConcentration of MeasureStochastic OptimizationRandomized OptimizationLinear Quadratic Gaussian