POSITIVE-DEFINITE MEMORYLESS SYMMETRIC RANK ONE METHOD FOR LARGE-SCALE UNCONSTRAINED OPTIMIZATION

CSpace

	POSITIVE-DEFINITE MEMORYLESS SYMMETRIC RANK ONE METHOD FOR LARGE-SCALE UNCONSTRAINED OPTIMIZATION
	Leong, Wah June 1,2; Abu Hassan, Malik 1
	2011
发表期刊	PACIFIC JOURNAL OF OPTIMIZATION
ISSN	1348-9151
卷号	7 期号:1 页码:29-41
摘要	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.
关键词	large-scale unconstrained optimization symmetric rank one method memoryless method optimal scaling
语种	英语
WOS研究方向	Operations Research & Management Science ; Mathematics
WOS类目	Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000288184500004
出版者	YOKOHAMA PUBL
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12531
专题	中国科学院数学与系统科学研究院
通讯作者	Leong, Wah June
作者单位	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
推荐引用方式 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.