A subspace implementation of quasi-Newton trust region methods for unconstrained optimization

doi:10.1007/s00211-006-0021-6

	A subspace implementation of quasi-Newton trust region methods for unconstrained optimization
	Wang, Zhou-Hong ; Yuan, Ya-Xiang
	2006-08-01
发表期刊	NUMERISCHE MATHEMATIK
ISSN	0029-599X
卷号	104 期号:2 页码:241-269
摘要	This paper studies subspace properties of trust region methods for unconstrained optimization, assuming the approximate Hessian is updated by quasi- Newton formulae and the initial Hessian approximation is appropriately chosen. It is shown that the trial step obtained by solving the trust region subproblem is in the subspace spanned by all the gradient vectors computed. Thus, the trial step can be defined by minimizing the quasi-Newton quadratic model in the subspace. Based on this observation, some subspace trust region algorithms are proposed and numerical results are also reported.
DOI	10.1007/s00211-006-0021-6
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000240310600005
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/2648
专题	计算数学与科学工程计算研究所
通讯作者	Wang, Zhou-Hong
作者单位	1.Chinese Acad Sci, Inst computat Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100080, Peoples R China 2.Beijing Jiaotong Univ, Dept Math, Beijing 100044, Peoples R China
推荐引用方式 GB/T 7714	Wang, Zhou-Hong,Yuan, Ya-Xiang. A subspace implementation of quasi-Newton trust region methods for unconstrained optimization[J]. NUMERISCHE MATHEMATIK,2006,104(2):241-269.
APA	Wang, Zhou-Hong,&Yuan, Ya-Xiang.(2006).A subspace implementation of quasi-Newton trust region methods for unconstrained optimization.NUMERISCHE MATHEMATIK,104(2),241-269.
MLA	Wang, Zhou-Hong,et al."A subspace implementation of quasi-Newton trust region methods for unconstrained optimization".NUMERISCHE MATHEMATIK 104.2(2006):241-269.