KMS Of Academy of mathematics and systems sciences, CAS
A null-space primal-dual interior-point algorithm for nonlinear optimization with nice convergence properties | |
Liu, Xinwei1; Yuan, Yaxiang2 | |
2010-09-01 | |
Source Publication | MATHEMATICAL PROGRAMMING |
ISSN | 0025-5610 |
Volume | 125Issue:1Pages:163-193 |
Abstract | 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. |
Keyword | 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 |
Language | 英语 |
Funding Project | 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 Research Area | Computer Science ; Operations Research & Management Science ; Mathematics |
WOS Subject | Computer Science, Software Engineering ; Operations Research & Management Science ; Mathematics, Applied |
WOS ID | WOS:000281761500008 |
Publisher | SPRINGER |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/11079 |
Collection | 计算数学与科学工程计算研究所 |
Corresponding Author | Yuan, Yaxiang |
Affiliation | 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 |
Recommended Citation 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. |
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