Explicit reformulations for robust optimization problems with general uncertainty sets

doi:10.1137/060650003

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	Explicit reformulations for robust optimization problems with general uncertainty sets
	Averbakh, Igor 1; Zhao, Yun-Bin 2
	2007
发表期刊	SIAM JOURNAL ON OPTIMIZATION
ISSN	1052-6234
卷号	18 期号:4 页码:1436-1466
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.
关键词	robust optimization data uncertainty mathematical programming homogeneous functions convex analysis
DOI	10.1137/060650003
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000253017400015
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/4713
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.