| 广义拟牛顿算法对一般目标函数的收敛性 |
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| 引用本文： | 陈兰平,王丽伟.广义拟牛顿算法对一般目标函数的收敛性[J].应用数学,2002,15(3):69-75. |
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| 作者姓名： | 陈兰平 王丽伟 |
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| 作者单位： | 首都师范大学数学系,北京,100037 |
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| 基金项目： | 北京市教委科研基金资助项目 (99KJ10 ) |
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| 摘 要： | 本文证明了求解无约束最优化的广义拟牛顿算法在Goldstein非精确线搜索下对一般目标函数的全局收敛性，并在一定条件下证明了算法的局部超线性收敛性。
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| 关 键 词： | 无约束最优化 广义拟牛顿算法 Goldstein非精确线搜索 全局收敛 局部超线性收敛性 |
| 文章编号： | 1001-9847(2002)03-0069-07 |
| 修稿时间： | 2002年1月14日 |
Global Convergence of the Generalized Quasi-Newton Algorithm for General Objective Functions |
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| CHEN Lan ping,WANG Li wei.Global Convergence of the Generalized Quasi-Newton Algorithm for General Objective Functions[J].Mathematica Applicata,2002,15(3):69-75. |
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| Authors: | CHEN Lan ping WANG Li wei |
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| Abstract: | In this paper,we develop the Generalized Quasi Newton methods for unconstrained optimization which was formed in paper,and we use inexact line searches (Goldstein rule).These methods are globally convergent when applied to a general objective function under the weak condition,and are locally super linearly convergent when applied to a uniformly convex function whoes Hessian matrix G(x) is Lipschitz continuous in the neighborhood of the optimal solution point.So we develop the results of paper and . |
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| Keywords: | Unconstrained optimization Generalized Quasi Newton method Goldetein rule Global and superlinearly convergence |
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