多阶段随机线性问题的精确量化

IF 2.6 1区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Optimization Pub Date : 2024-02-05 DOI:10.1137/22m1508005

Maël Forcier, Stéphane Gaubert, Vincent Leclère

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引用次数: 0

摘要

SIAM 优化期刊》，第 34 卷，第 1 期，第 533-562 页，2024 年 3 月。摘要我们证明了具有任意成本分布的多阶段随机线性问题（MSLP）等价于有限情景树上的 MSLP。我们通过分析 MSLP 的多面体结构建立了这一精确量化结果。特别是，我们证明了预期成本-去向函数是多面体的，并且在室复数的单元上是仿射的，这与成本分布无关。这带来了新的复杂性结果，表明当某些参数固定时，MSLP 会变成多项式。

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Exact Quantization of Multistage Stochastic Linear Problems

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.

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来源期刊

SIAM Journal on Optimization 数学-应用数学

CiteScore

5.30

自引率

9.70%

发文量

101

审稿时长

6-12 weeks

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.