A null-space primal-dual interior-point algorithm for nonlinear optimization with nice convergence properties

doi:10.1007/s10107-009-0272-y

	A null-space primal-dual interior-point algorithm for nonlinear optimization with nice convergence properties
	Liu, Xinwei 1; Yuan, Yaxiang2
	2010-09-01
发表期刊	MATHEMATICAL PROGRAMMING
ISSN	0025-5610
卷号	125 期号:1 页码:163-193
摘要	We present a null-space primal-dual interior-point algorithm for solving nonlinear optimization problems with general inequality and equality constraints. The algorithm approximately solves a sequence of equality constrained barrier subproblems by computing a range-space step and a null-space step in every iteration. The a""(2) penalty function is taken as the merit function. Under very mild conditions on range-space steps and approximate Hessians, without assuming any regularity, it is proved that either every limit point of the iterate sequence is a Karush-Kuhn-Tucker point of the barrier subproblem and the penalty parameter remains bounded, or there exists a limit point that is either an infeasible stationary point of minimizing the a"" (2) norm of violations of constraints of the original problem, or a Fritz-John point of the original problem. In addition, we analyze the local convergence properties of the algorithm, and prove that by suitably controlling the exactness of range-space steps and selecting the barrier parameter and Hessian approximation, the algorithm generates a superlinearly or quadratically convergent step. The conditions on guaranteeing that all slack variables are still positive for a full step are presented.
关键词	Global and local convergences Null-space technique Primal-dual interior-point methods Nonlinear optimization with inequality and equality constraints
DOI	10.1007/s10107-009-0272-y
语种	英语
资助项目	National Natural Science Foundation of China[10571039] ; National Natural Science Foundation of China[10231060] ; National Natural Science Foundation of China[10831006] ; Hebei University of Technology
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:000281761500008
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/11079
专题	计算数学与科学工程计算研究所
通讯作者	Yuan, Yaxiang
作者单位	1.Hebei Univ Technol, Dept Appl Math, Tianjin, Peoples R China 2.Chinese Acad Sci, LSEC, Acad Math & Syst Sci, 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 null-space primal-dual interior-point algorithm for nonlinear optimization with nice convergence properties[J]. MATHEMATICAL PROGRAMMING,2010,125(1):163-193.
APA	Liu, Xinwei,&Yuan, Yaxiang.(2010).A null-space primal-dual interior-point algorithm for nonlinear optimization with nice convergence properties.MATHEMATICAL PROGRAMMING,125(1),163-193.
MLA	Liu, Xinwei,et al."A null-space primal-dual interior-point algorithm for nonlinear optimization with nice convergence properties".MATHEMATICAL PROGRAMMING 125.1(2010):163-193.