A trust region method for optimization problem with singular solutions

doi:10.1007/s00245-007-9009-6

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	A trust region method for optimization problem with singular solutions
	Zhang, Juliang ; Wu, Liangyun ; Zhang, Xiangsun
	2007-12-01
发表期刊	APPLIED MATHEMATICS AND OPTIMIZATION
ISSN	0095-4616
卷号	56 期号:3 页码:379-394
摘要	In this paper, we propose a trust region method for minimizing a function whose Hessian matrix at the solutions may be singular. The global convergence of the method is obtained under mild conditions. Moreover, we show that if the objective function is LC2 function, the method possesses local superlinear convergence under the local error bound condition without the requirement of isolated nonsingular solution. This is the first regularized Newton method with trust region technique which possesses local superlinear (quadratic) convergence without the assumption that the Hessian of the objective function at the solution is nonsingular. Preliminary numerical experiments show the efficiency of the method.
关键词	nonlinear convex optimization trust region method local error bound superlinear convergence nonsingularity
DOI	10.1007/s00245-007-9009-6
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000251235100005
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/4214
专题	应用数学研究所
通讯作者	Zhang, Juliang
作者单位	1.Jiao Tong Univ, Sch Econ & Management, Res Inst Mat Flow, Beijing 100044, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Juliang,Wu, Liangyun,Zhang, Xiangsun. A trust region method for optimization problem with singular solutions[J]. APPLIED MATHEMATICS AND OPTIMIZATION,2007,56(3):379-394.
APA	Zhang, Juliang,Wu, Liangyun,&Zhang, Xiangsun.(2007).A trust region method for optimization problem with singular solutions.APPLIED MATHEMATICS AND OPTIMIZATION,56(3),379-394.
MLA	Zhang, Juliang,et al."A trust region method for optimization problem with singular solutions".APPLIED MATHEMATICS AND OPTIMIZATION 56.3(2007):379-394.