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
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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 |
DOI | 10.1007/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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