KMS Of Academy of mathematics and systems sciences, CAS
| POSITIVE-DEFINITE MEMORYLESS SYMMETRIC RANK ONE METHOD FOR LARGE-SCALE UNCONSTRAINED OPTIMIZATION | |
| Leong, Wah June1,2; Abu Hassan, Malik1 | |
| 2011 | |
| Source Publication | PACIFIC JOURNAL OF OPTIMIZATION
 |
| ISSN | 1348-9151 |
| Volume | 7Issue:1Pages:29-41 |
| Abstract | Memoryless quasi-Newton method is exactly the quasi-Newton method for which the approximation to the inverse of Hessian, at each step, is updated from a positive multiple of identity matrix. Hence its search direction can be computed without the storage of matrices, namely O(n(2))storages.In this paper, a memoryless symmetric rank one (SR1) method for solving large-scale unconstrained optimization problems is presented. The basic idea is to incorporate the SR1 update within the framework of the memoryless quasi-Newton method. However, it is well-known that the SR1 update may not preserve positive definiteness even when updated from a positive definite matrix. Therefore, we propose that the memoryless SR1 method is updated from a positive scaled of the identity, in which the scaling factor is derived in such a way to preserve the positive definiteness and improves the condition of the scaled memoryless SR1 update. Under some standard conditions it is shown that the method is globally and R linearly convergent. Numerical results show that the memoryless SR1 method is very encouraging. |
| Keyword | large-scale unconstrained optimization symmetric rank one method memoryless method optimal scaling |
| Language | 英语 |
| WOS Research Area | Operations Research & Management Science ; Mathematics |
| WOS Subject | Operations Research & Management Science ; Mathematics, Applied |
| WOS ID | WOS:000288184500004 |
| Publisher | YOKOHAMA PUBL |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/12531 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Leong, Wah June |
| Affiliation | 1.Univ Putra Malaysia, Inst Math Res, Serdang 43400, Selangor, Malaysia 2.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100864, Peoples R China |
| Recommended Citation GB/T 7714 | Leong, Wah June,Abu Hassan, Malik. POSITIVE-DEFINITE MEMORYLESS SYMMETRIC RANK ONE METHOD FOR LARGE-SCALE UNCONSTRAINED OPTIMIZATION[J]. PACIFIC JOURNAL OF OPTIMIZATION,2011,7(1):29-41. |
| APA | Leong, Wah June,&Abu Hassan, Malik.(2011).POSITIVE-DEFINITE MEMORYLESS SYMMETRIC RANK ONE METHOD FOR LARGE-SCALE UNCONSTRAINED OPTIMIZATION.PACIFIC JOURNAL OF OPTIMIZATION,7(1),29-41. |
| MLA | Leong, Wah June,et al."POSITIVE-DEFINITE MEMORYLESS SYMMETRIC RANK ONE METHOD FOR LARGE-SCALE UNCONSTRAINED OPTIMIZATION".PACIFIC JOURNAL OF OPTIMIZATION 7.1(2011):29-41. |
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