{"title":"Exact Quantization of Multistage Stochastic Linear Problems","authors":"Maël Forcier, Stéphane Gaubert, Vincent Leclère","doi":"10.1137/22m1508005","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Optimization, Volume 34, Issue 1, Page 533-562, March 2024. <br/> Abstract. We show that the multistage stochastic linear problem (MSLP) with an arbitrary cost distribution is equivalent to an MSLP on a finite scenario tree. We establish this exact quantization result by analyzing the polyhedral structure of MSLPs. In particular, we show that the expected cost-to-go functions are polyhedral and affine on the cells of a chamber complex, which is independent of the cost distribution. This leads to new complexity results, showing that MSLP becomes polynomial when certain parameters are fixed.","PeriodicalId":49529,"journal":{"name":"SIAM Journal on Optimization","volume":"69 1","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Optimization","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/22m1508005","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
SIAM Journal on Optimization, Volume 34, Issue 1, Page 533-562, March 2024. Abstract. We show that the multistage stochastic linear problem (MSLP) with an arbitrary cost distribution is equivalent to an MSLP on a finite scenario tree. We establish this exact quantization result by analyzing the polyhedral structure of MSLPs. In particular, we show that the expected cost-to-go functions are polyhedral and affine on the cells of a chamber complex, which is independent of the cost distribution. This leads to new complexity results, showing that MSLP becomes polynomial when certain parameters are fixed.
期刊介绍：
The SIAM Journal on Optimization contains research articles on the theory and practice of optimization. The areas addressed include linear and quadratic programming, convex programming, nonlinear programming, complementarity problems, stochastic optimization, combinatorial optimization, integer programming, and convex, nonsmooth and variational analysis. Contributions may emphasize optimization theory, algorithms, software, computational practice, applications, or the links between these subjects.
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