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A trust region method for optimization problem with singular solutions

文献类型：期刊论文

作者Zhang, Juliang; Wu, Liangyun; Zhang, Xiangsun
刊名APPLIED MATHEMATICS AND OPTIMIZATION
出版日期2007-12-01
卷号56期号:3页码:379-394
关键词nonlinear convex optimization trust region method local error bound superlinear convergence nonsingularity
ISSN号0095-4616
DOI10.1007/s00245-007-9009-6
英文摘要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.
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000251235100005
出版者SPRINGER
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/4213]  
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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