FEASIBLE METHOD FOR SEMI-INFINITE PROGRAMS

doi:10.1137/140982143

	FEASIBLE METHOD FOR SEMI-INFINITE PROGRAMS
	Wang, Shuxiong; Yuan, Yaxiang
	2015
发表期刊	SIAM JOURNAL ON OPTIMIZATION
ISSN	1052-6234
卷号	25 期号:4 页码:2537-2560
摘要	A new numerical method is presented for semi-infinite optimization problems which guarantees that each iterate is feasible for the original problem. The basic idea is to construct concave relaxations of the lower level problem, to compute the optimal values of the relaxation problems explicitly, and to solve the resulting approximate problems with finitely many constraints. The concave relaxations are constructed by replacing the objective function of the lower level problem by its concave upper bound functions. Under mild conditions, we prove that every accumulation point of the solutions of the approximate problems is an optimal solution of the original problem. An adaptive subdivision algorithm is proposed to solve semi-infinite optimization problems. It is shown that the Karush-Kuhn-Tucker points of the approximate problems converge to a Karush-Kuhn-Tucker point of the original problem within arbitrarily given tolerances. Numerical experiments show that our algorithm is much faster than the existing adaptive convexification algorithm in computation time.
关键词	semi-infinite programs concave optimization adaptive subdivision algorithm
DOI	10.1137/140982143
语种	英语
资助项目	NSFC[11331012] ; NSFC[11321061] ; NSFC[11461161005]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000367019700023
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/21591
专题	计算数学与科学工程计算研究所
通讯作者	Wang, Shuxiong
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Wang, Shuxiong,Yuan, Yaxiang. FEASIBLE METHOD FOR SEMI-INFINITE PROGRAMS[J]. SIAM JOURNAL ON OPTIMIZATION,2015,25(4):2537-2560.
APA	Wang, Shuxiong,&Yuan, Yaxiang.(2015).FEASIBLE METHOD FOR SEMI-INFINITE PROGRAMS.SIAM JOURNAL ON OPTIMIZATION,25(4),2537-2560.
MLA	Wang, Shuxiong,et al."FEASIBLE METHOD FOR SEMI-INFINITE PROGRAMS".SIAM JOURNAL ON OPTIMIZATION 25.4(2015):2537-2560.