A SEQUENTIAL QUADRATIC PROGRAMMING METHOD WITHOUT A PENALTY FUNCTION OR A FILTER FOR NONLINEAR EQUALITY CONSTRAINED OPTIMIZATION

doi:10.1137/080739884

	A SEQUENTIAL QUADRATIC PROGRAMMING METHOD WITHOUT A PENALTY FUNCTION OR A FILTER FOR NONLINEAR EQUALITY CONSTRAINED OPTIMIZATION
	Liu, Xinwei 1; Yuan, Yaxiang2
	2011
发表期刊	SIAM JOURNAL ON OPTIMIZATION
ISSN	1052-6234
卷号	21 期号:2 页码:545-571
摘要	We present a sequential quadratic programming method without using a penalty function or a filter for solving nonlinear equality constrained optimization. In each iteration, the linearized constraints of the quadratic programming are relaxed to satisfy two mild conditions; the step-size is selected such that either the value of the objective function or the measure of the constraint violations is sufficiently reduced. As a result, our method has two nice properties. First, we do not need to assume the boundedness of the iterative sequence. Second, we do not need any restoration phase which is necessary for filter methods. We prove that the algorithm will terminate at either an approximate Karush-Kuhn-Tucker point, an approximate Fritz-John point, or an approximate infeasible stationary point which is an approximate stationary point for minimizing the l 2 norm of the constraint violations. By controlling the exactness of the linearized constraints and introducing a second-order correction technique, without requiring linear independence constraint qualification, the algorithm is shown to be locally superlinearly convergent. The preliminary numerical results show that the algorithm is robust and efficient when solving some small-and medium-sized problems from the CUTE collection.
关键词	sequential quadratic programming penalty function filter regularity global and local convergence analysis
DOI	10.1137/080739884
语种	英语
资助项目	National Natural Science Foundation of China[10971047] ; National Natural Science Foundation of China[10831006] ; Hebei Natural Science Foundation of China[A2010000011] ; CAS[kjcx-yw-s7]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000292247200006
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/12328
专题	计算数学与科学工程计算研究所
通讯作者	Liu, Xinwei
作者单位	1.Hebei Univ Technol, Dept Appl Math, Tianjin 300401, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp LSEC, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Liu, Xinwei,Yuan, Yaxiang. A SEQUENTIAL QUADRATIC PROGRAMMING METHOD WITHOUT A PENALTY FUNCTION OR A FILTER FOR NONLINEAR EQUALITY CONSTRAINED OPTIMIZATION[J]. SIAM JOURNAL ON OPTIMIZATION,2011,21(2):545-571.
APA	Liu, Xinwei,&Yuan, Yaxiang.(2011).A SEQUENTIAL QUADRATIC PROGRAMMING METHOD WITHOUT A PENALTY FUNCTION OR A FILTER FOR NONLINEAR EQUALITY CONSTRAINED OPTIMIZATION.SIAM JOURNAL ON OPTIMIZATION,21(2),545-571.
MLA	Liu, Xinwei,et al."A SEQUENTIAL QUADRATIC PROGRAMMING METHOD WITHOUT A PENALTY FUNCTION OR A FILTER FOR NONLINEAR EQUALITY CONSTRAINED OPTIMIZATION".SIAM JOURNAL ON OPTIMIZATION 21.2(2011):545-571.