A framework of constraint preserving update schemes for optimization on Stiefel manifold
文献类型：期刊论文
| 作者 | Jiang, Bo; Dai, Yu-Hong
|
| 刊名 | MATHEMATICAL PROGRAMMING
 |
| 出版日期 | 2015-11-01 |
| 卷号 | 153期号:2页码:535-575 |
| 关键词 | Stiefel manifold Orthogonality constraint Sphere constraint Range space Null space Barzilai-Borwein-like method Feasible Adaptive nonmonotone line search Low-rank correlation matrix Kohn-Sham total energy minimization Heterogeneous quadratic functions |
| ISSN号 | 0025-5610 |
| DOI | 10.1007/s10107-014-0816-7 |
| 英文摘要 | This paper considers optimization problems on the Stiefel manifold (XX)-X-T = I-p, where X is an element of R-nxp is the variable and I-p is the p-by-p identity matrix. A framework of constraint preserving update schemes is proposed by decomposing each feasible point into the range space of X and the null space of X-T. While this general framework can unify many existing schemes, a new update scheme with low complexity cost is also discovered. Then we study a feasible Barzilai-Borwein-like method under the new update scheme. The global convergence of the method is established with an adaptive nonmonotone line search. The numerical tests on the nearest low-rank correlation matrix problem, the Kohn-Sham total energy minimization and a specific problem from statistics demonstrate the efficiency of the new method. In particular, the new method performs remarkably well for the nearest low-rank correlation matrix problem in terms of speed and solution quality and is considerably competitive with the widely used SCF iteration for the Kohn-Sham total energy minimization. |
| 资助项目 | National Key Basic Research Program of China[2015CB856000] ; China National Funds for Distinguished Young Scientists[11125107] ; Chinese NSF[10831106] ; Chinese NSF[81211130105] ; CAS grant[kjcx-yw-s7-03] |
| WOS研究方向 | Computer Science ; Operations Research & Management Science ; Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000364330300010 |
| 出版者 | SPRINGER HEIDELBERG |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/21156]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Dai, Yu-Hong |
| 作者单位 | Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Jiang, Bo,Dai, Yu-Hong. A framework of constraint preserving update schemes for optimization on Stiefel manifold[J]. MATHEMATICAL PROGRAMMING,2015,153(2):535-575. |
| APA | Jiang, Bo,&Dai, Yu-Hong.(2015).A framework of constraint preserving update schemes for optimization on Stiefel manifold.MATHEMATICAL PROGRAMMING,153(2),535-575. |
| MLA | Jiang, Bo,et al."A framework of constraint preserving update schemes for optimization on Stiefel manifold".MATHEMATICAL PROGRAMMING 153.2(2015):535-575. |
入库方式： OAI收割
来源：数学与系统科学研究院
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