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Explicit reformulations for robust optimization problems with general uncertainty sets

文献类型：期刊论文

作者Averbakh, Igor1; Zhao, Yun-Bin2
刊名SIAM JOURNAL ON OPTIMIZATION
出版日期2007
卷号18期号:4页码:1436-1466
关键词robust optimization data uncertainty mathematical programming homogeneous functions convex analysis
ISSN号1052-6234
DOI10.1137/060650003
英文摘要We consider a rather general class of mathematical programming problems with data uncertainty, where the uncertainty set is represented by a system of convex inequalities. We prove that the robust counterparts of this class of problems can be reformulated equivalently as finite and explicit optimization problems. Moreover, we develop simplified reformulations for problems with uncertainty sets defined by convex homogeneous functions. Our results provide a unified treatment of many situations that have been investigated in the literature and are applicable to a wider range of problems and more complicated uncertainty sets than those considered before. The analysis in this paper makes it possible to use existing continuous optimization algorithms to solve more complicated robust optimization problems. The analysis also shows how the structure of the resulting reformulation of the robust counterpart depends both on the structure of the original nominal optimization problem and on the structure of the uncertainty set.
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000253017400015
出版者SIAM PUBLICATIONS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/4712]  
专题中国科学院数学与系统科学研究院
通讯作者Averbakh, Igor
作者单位1.Univ Toronto, Div Management, Scarborough, ON M1C 1A4, Canada
2.Chinese Acad Sci, AMSS, Inst Appl Math, Beijing 100080, Peoples R China
推荐引用方式
GB/T 7714		 Averbakh, Igor,Zhao, Yun-Bin. Explicit reformulations for robust optimization problems with general uncertainty sets[J]. SIAM JOURNAL ON OPTIMIZATION,2007,18(4):1436-1466.
APA Averbakh, Igor,&Zhao, Yun-Bin.(2007).Explicit reformulations for robust optimization problems with general uncertainty sets.SIAM JOURNAL ON OPTIMIZATION,18(4),1436-1466.
MLA Averbakh, Igor,et al."Explicit reformulations for robust optimization problems with general uncertainty sets".SIAM JOURNAL ON OPTIMIZATION 18.4(2007):1436-1466.

入库方式： OAI收割

来源：数学与系统科学研究院

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