| The Substitution Secant/Finite Difference Method for Large Scale Sparse Unconstrained Optimization |
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| 作者姓名： | Hong-wei Zhang Jun-xiang Li |
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| 作者单位： | Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China |
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| 基金项目： | Supported by the National Natural Science Foundation of China （No.10471015） and the State Foundation of Ph.D Units of China （No.20020141013） |
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| 摘 要： | This paper studies a substitution secant/finite difference （SSFD） method for solving large scale sparse unconstrained optimization problems. This method is a combination of a secant method and a finite difference method, which depends on a consistent partition of the columns of the lower triangular part of the Hessian matrix. A q-superlinear convergence result and an r-convergence rate estimate show that this method has good local convergence properties. The numerical results show that this method may be competitive with some currently used algorithms.
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| 关 键 词： | 无约束最优化 置换算法 有限微分 正切法 SSFD Hessian矩阵 |
| 收稿时间： | 2004-03-13 |
| 修稿时间： | 2004-03-132005-06-24 |
The Substitution Secant/Finite Difference Method for Large Scale Sparse Unconstrained Optimization |
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| Hong-wei Zhang Jun-xiang Li.The Substitution Secant/Finite Difference Method for Large Scale Sparse Unconstrained Optimization[J].Acta Mathematicae Applicatae Sinica,2005,21(4):581-596. |
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| Authors: | Hong-wei Zhang Jun-xiang Li |
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| Institution: | (1) Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China |
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| Abstract: | Abstract
This paper studies a substitution secant/finite difference (SSFD) method for solving large scale sparse unconstrained optimization
problems. This method is a combination of a secant method and a finite difference method, which depends on a consistent partition
of the columns of the lower triangular part of the Hessian matrix. A q-superlinear convergence result and an r-convergence rate estimate show that this method has good local convergence properties. The numerical results show that this
method may be competitive with some currently used algorithms.
Supported by the National Natural Science Foundation of China (No.10471015) and the State Foundation of Ph.D Units of China
(No.20020141013) |
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| Keywords: | Unconstrained optimization substitution Hessian sparsity secant method |
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