| 带非精确线搜索广义Broyden族的收敛性质 |
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| 引用本文： | 柯小伍.带非精确线搜索广义Broyden族的收敛性质[J].北京师范大学学报(自然科学版),1999,35(1):22-27. |
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| 作者姓名： | 柯小伍 |
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| 作者单位： | 北京师范大学数学系,100875,北京 |
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| 摘 要： | 提出了一个新的函数，并给出了此函数的性质，利用它们分析广义Ｂｒｏｙｄｅｎ族。在较弱的条件下，对一致凸函数的无约束最优化问题，证明了带非精确线搜索的广义Ｂｒｏｙｄｅｎ族的全局和超线性收敛性，而且在较弱的条件下，证明了Ｂｒｏｙｄｅｎ族的全局和超线性收敛性。
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| 关 键 词： | 无约束最优化 拟牛顿法 广义Broyden族 全局和超线性收敛性 一致凸函数 |
| 修稿时间： | 1998-09-1023 |
CONVERGENCE PROPERTIES OF GENERALIZED BROYDEN'S FAMILY WITH INEXACT LINESE ARCHES |
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| KeXiaowu.CONVERGENCE PROPERTIES OF GENERALIZED BROYDEN''''S FAMILY WITH INEXACT LINESE ARCHES[J].Journal of Beijing Normal University(Natural Science),1999,35(1):22-27. |
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| Authors: | KeXiaowu |
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| Institution: | KeXiaowu
(Department of Mathematics,Beijing Normal University,100875,Beijing,China) |
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| Abstract: | A new function is proposed. Some properties of this function are presental. Thebehavior of generalized Broyden's family is analyzed by using these properties. Under mild conditions, it is proved the global and saperlinear convergence of generalized Broyden's family withinexact line searches on uniformly convex function. Moreover, under weak conditions, theglobal and superlinear convergence of Broyden's family is proved. |
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| Keywords: | unconshained optimization quasi-Newton method generalized Broyden's family global and superlinear convergences uniformly convex function |
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