On a new homotopy continuation trajectory for nonlinear complementarity problems
文献类型：期刊论文
| 作者 | Zhao, YB; Li, D |
| 刊名 | MATHEMATICS OF OPERATIONS RESEARCH
 |
| 出版日期 | 2001-02-01 |
| 卷号 | 26期号:1页码:119-146 |
| ISSN号 | 0364-765X |
| 关键词 | complementarity problems continuation methods homotopy continuation trajectories strictly feasible condition P-0-functions P*-functions |
| 英文摘要 | Most known continuation methods for P-0 complementarity problems require some restrictive assumptions, such as the strictly feasible condition and the properness condition, to guarantee the existence and the boundedness of certain homotopy continuation trajectory. To relax such restrictions, we propose a new homotopy formulation for the complementarity problem based on which a new homotopy continuation trajectory is generated. For P-0 complementarity problems, the most promising feature of this trajectory is the assurance of the existence and the boundedness of the trajectory under a condition that is strictly weaker than the standard ones used widely in the literature of continuation methods. Particularly, the often-assumed strictly feasible condition is not required here. When applied to P* complementarity problems, the boundedness of the proposed trajectory turns out to be equivalent to the solvability of the problem, and the entire trajectory converges to the (unique) least element solution provided that it exists. Moreover, for monotone complementarity problems, the whole trajectory always converges to a least 2-norm solution provided that the solution set of the problem is nonempty. The results presented in this paper can serve as a theoretical basis for constructing a new path-following algorithm for solving complementarity problems, even for the situations where the solution set is unbounded. |
| WOS研究方向 | Operations Research & Management Science ; Mathematics |
| 语种 | 英语 |
| 出版者 | INST OPERATIONS RESEARCH MANAGEMENT SCIENCES |
| WOS记录号 | WOS:000167548300009 |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/16764]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Zhao, YB |
| 作者单位 | 1.Chinese Univ Hong Kong, Dept Syst Engn & Engn Management, Shatin, Hong Kong, Peoples R China 2.Chinese Acad Sci, Inst Appl Math, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Zhao, YB,Li, D. On a new homotopy continuation trajectory for nonlinear complementarity problems[J]. MATHEMATICS OF OPERATIONS RESEARCH,2001,26(1):119-146. |
| APA | Zhao, YB,&Li, D.(2001).On a new homotopy continuation trajectory for nonlinear complementarity problems.MATHEMATICS OF OPERATIONS RESEARCH,26(1),119-146. |
| MLA | Zhao, YB,et al."On a new homotopy continuation trajectory for nonlinear complementarity problems".MATHEMATICS OF OPERATIONS RESEARCH 26.1(2001):119-146. |
入库方式： OAI收割
来源：数学与系统科学研究院
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