| 改进的SR1拟牛顿法的2n步q二次收敛性 |
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| 引用本文： | 李换琴,徐成贤.改进的SR1拟牛顿法的2n步q二次收敛性[J].西安交通大学学报,2000,34(8):100-103. |
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| 作者姓名： | 李换琴 徐成贤 |
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| 作者单位： | 西安交通大学,710049,西安 |
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| 基金项目： | 国家自然科学基金资助项目(19971065)． |
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| 摘 要： | 为了从理论上证明基于新拟牛顿方程的改进拟牛顿方法比传统的拟牛顿方法有更好的收敛效果，对改进的ＳＲ１拟牛顿方法进行了深入的研究，在变尺度矩阵序列正定有界的条件下，证明了算法在每ｎ＋ｐ（ｐ≥１）步迭代中至少有ｐ步是好的（ｑ超线性步），进而证明了算法的２ｎ步ｑ二次收敛性。
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| 关 键 词： | 拟牛顿方程 收敛性 SR1拟牛顿法 无约束最优化 |
| 文章编号： | 0253-987X(2000)08-0100-04 |
| 修稿时间： | 1999-12-26 |
Convergence of Quasi-Newton Method by Modified SR1 Update |
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| Li Huanqin,Xu Chengxian.Convergence of Quasi-Newton Method by Modified SR1 Update[J].Journal of Xi'an Jiaotong University,2000,34(8):100-103. |
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| Authors: | Li Huanqin Xu Chengxian |
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| Institution: | Li Huanqin
,Xu Chengxian
;(Xi'an Jiaotong University, Xi'an 710049, China) |
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| Abstract: | In order to shown some superiority of the modified quasi Newton methods based on the new quasi Newton equations over the usual quasi Newton methods from the theoretical point of view, A symmetric rank one method that satisfies the new quasi Newton equation is investigated. It is proved that this algorithm generates at least p q superlinear steps out of every n p steps, and hence the convergence rate is 2 n step q quadratic under the condition that the sequence of variable metric matrices is positive definite and uniformly bounded. |
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| Keywords: | new quasi-Newton method SR1 update convergence |
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