A null-space primal-dual interior-point algorithm for nonlinear optimization with nice convergence properties
文献类型：期刊论文
| 作者 | Liu, Xinwei1; Yuan, Yaxiang2
|
| 刊名 | MATHEMATICAL PROGRAMMING
 |
| 出版日期 | 2010-09-01 |
| 卷号 | 125期号:1页码:163-193 |
| 关键词 | Global and local convergences Null-space technique Primal-dual interior-point methods Nonlinear optimization with inequality and equality constraints |
| ISSN号 | 0025-5610 |
| DOI | 10.1007/s10107-009-0272-y |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000281761500008 |
| 出版者 | SPRINGER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/11078]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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