| A GENERALIZED QUASI-NEWTON EQUATION AND COMPUTATIONAL EXPERIENCE |
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| 作者姓名： | Lei-hong Zhang Ping-qi Pan |
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| 作者单位： | Department of Mathematics，Southeast University，Nanjing 210096，China |
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| 基金项目： | Project 10371017 supported by National Natural Science Foundation of China. |
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| 摘 要： | The quasi-Newton equation has played a central role in the quasi-Newton methods forsolving systems of nonlinear equations and/or unconstrained optimization problems.In-stead,Pan suggested a new equation,and showed that it is of the second order while thetraditional of the first order,in certain approximation sense12].In this paper,we makea generalization of the two equations to include them as special cases.The generalizedequation is analyzed,and new updates are derived from it.A DFP-like new update out-performed the traditional DFP update in computational experiments on a set of standardtest problems.
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| 关 键 词： | 非线性系统方程 非拘束最优化 二阶准牛顿方程 更新公式 |
| 收稿时间： | 2005-03-30 |
| 修稿时间： | 2005-03-302005-12-14 |
A GENERALIZED QUASI-NEWTON EQUATION AND COMPUTATIONAL EXPERIENCE |
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| Lei-hong Zhang Ping-qi Pan.A GENERALIZED QUASI-NEWTON EQUATION AND COMPUTATIONAL EXPERIENCE[J].Journal of Computational Mathematics,2006,24(5):665-674. |
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| Authors: | Lei-hong Zhang Ping-qi Pan |
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| Abstract: | The quasi-Newton equation has played a central role in the quasi-Newton methods for solving systems of nonlinear equations and/or unconstrained optimization problems.In- stead,Pan suggested a new equation,and showed that it is of the second order while the traditional of the first order,in certain approximation sense12].In this paper,we make a generalization of the two equations to include them as special cases.The generalized equation is analyzed,and new updates are derived from it.A DFP-like new update out- performed the traditional DFP update in computational experiments on a set of standard test problems. |
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| Keywords: | System of nonlinear equations Unconstrained optimization Quasi-Newton equation Second-order Quasi-Newton equation Update formula |
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