Multipolar robust optimization

被引:7
作者
Ben-Ameur, Walid [1 ]
Ouorou, Adam [2 ]
Wang, Guanglei [1 ,2 ]
Zotkiewicz, Mateusz [3 ]
机构
[1] Univ Paris Saclay, CNRS, Telecom SudParis, Samovar, 9 Rue Charles Fourier, F-91011 Evry, France
[2] Orange Labs Res, 38-40 Rue Gen Leclerc, F-92794 Issy Les Moulineaux 9, France
[3] Warsaw Univ Technol, Inst Telecommun, Nowowiejska 15-19, PL-00665 Warsaw, Poland
关键词
Uncertainty; Robust optimization; Multistage optimization; Polyhedral approximation;
D O I
10.1007/s13675-017-0092-4
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
We consider linear programs involving uncertain parameters and propose a new tractable robust counterpart which contains and generalizes several other models including the existing Affinely Adjustable Robust Counterpart and the Fully Adjustable Robust Counterpart. It consists in selecting a set of poles whose convex hull contains some projection of the uncertainty set, and computing a recourse strategy for each data scenario as a convex combination of some optimized recourses (one for each pole). We show that the proposed multipolar robust counterpart is tractable and its complexity is controllable. Further, we show that under some mild assumptions, two sequences of upper and lower bounds converge to the optimal value of the fully adjustable robust counterpart. We numerically investigate a couple of applications in the literature demonstrating that the approach can effectively improve the affinely adjustable policy.
引用
收藏
页码:395 / 434
页数:40
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