Global optimization in Hilbert space

doi:10.1007/s10107-017-1215-7

	Global optimization in Hilbert space
	Houska, Boris1 ; Chachuat, Benoit 2
	2019-01
发表期刊	MATHEMATICAL PROGRAMMING
ISSN	0025-5610
卷号	173 期号:1-2 页码:221-249
发表状态	已发表
DOI	10.1007/s10107-017-1215-7
摘要	We propose a complete-search algorithm for solving a class of non-convex, possibly infinite-dimensional, optimization problems to global optimality. We assume that the optimization variables are in a bounded subset of a Hilbert space, and we determine worst-case run-time bounds for the algorithm under certain regularity conditions of the cost functional and the constraint set. Because these run-time bounds are independent of the number of optimization variables and, in particular, are valid for optimization problems with infinitely many optimization variables, we prove that the algorithm converges to an epsilon-suboptimal global solution within finite run-time for any given termination tolerance epsilon>0. Finally, we illustrate these results for a problem of calculus of variations.
关键词	Infinite-dimensional optimization Complete search Branch-and-lift Convergence analysis Complexity analysis
收录类别	SCI ; SCIE ; EI
语种	英语
资助项目	Marie Curie Career Integration Grant[PCIG09-GA-2011-293953]
WOS研究方向	Computer Science ; Operations Research & Management Science ; Mathematics
WOS类目	Computer Science, Software Engineering ; Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000456970900007
出版者	SPRINGER HEIDELBERG
WOS关键词	CONVEX COMPUTATION ; APPROXIMATIONS ; INTERSECTION ; INTEGRATION ; ELLIPSOIDS ; ALGORITHM ; CUT ; SET
原始文献类型	Article
引用统计
文献类型	期刊论文
条目标识符	https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/29712
专题	信息科学与技术学院_PI研究组_Boris Houska组
通讯作者	Chachuat, Benoit
作者单位	1.ShanghaiTech Univ, Sch Informat Sci & Technol, 319 Yueyang Rd, Shanghai 200031, Peoples R China 2.Imperial Coll London, Ctr Proc Syst Engn, Dept Chem Engn, South Kensington Campus, London SW7 2AZ, England
第一作者单位	信息科学与技术学院
第一作者的第一单位	信息科学与技术学院
推荐引用方式 GB/T 7714	Houska, Boris,Chachuat, Benoit. Global optimization in Hilbert space[J]. MATHEMATICAL PROGRAMMING,2019,173(1-2):221-249.
APA	Houska, Boris,&Chachuat, Benoit.(2019).Global optimization in Hilbert space.MATHEMATICAL PROGRAMMING,173(1-2),221-249.
MLA	Houska, Boris,et al."Global optimization in Hilbert space".MATHEMATICAL PROGRAMMING 173.1-2(2019):221-249.