非单调带参数Perry-Shanno无记忆拟牛顿法的收敛性

doi:10.15960/j.cnki.issn.1007-6093.2016.04.010

Abstract

Abstract:

A nonmonotonic Perry-Shanno's memoryless Quasi-Newton method with parameters for unconstrained optimization is investigated.The global convergence of
this algorithm is proved for convex objective function when parameters are in the given range.

Key words: Perry-Shanno memoryless Quasi-Newton method, parameters, nonmonotone linesearch, global convergence

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HANG Dan, YAN Shijian. Convergence of nonmonotonic Perry-Shanno's memoryless quasi-Newton method with parameters[J]. Operations Research Transactions, 2016, 20(4): 85-92.

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URL: https://www.ort.shu.edu.cn/EN/10.15960/j.cnki.issn.1007-6093.2016.04.010

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References

[1] Perry J M. A class of conjugate gradient algorithms with a two step variable metric memory [D]. Evanston: Northwestern University, 1977.

[2] Shanno D F. On the convergence of a new conjugate gradient algorithm [J]. SIAM Journal on Numerical Analysis, 1978, 15(6): 1247-1257.

[3] Grippo L, Lampariello F, Lucidi S. A nonmonotone line search technique for Newton's method [J]. SIAM Journal on Numerical Analysis, 1986, {23}(4): 707-716.

[4] Han J, Liu G H. Global Convergence of a new nonmonotone BFGS algorithm on convex objective function [J]. Computational Optimization and Applications, 1997, 7(3): 277-289.

[5] Powel M J D. Restart procedures for the conjugate gradient method [J]. Mathematics Program, 1977, 12(1): 241-254.

[6] 颜世建. 一种无记忆拟牛顿法的收敛性 [J]. 南京师范大学学报(自然科学版}), 2004,27(2): 9-16.

[7] 袁亚湘. 非线性规划数值方法 [M]. 上海: 上海科技出版社, 1993.

[8] Han J, Liu G H, Yin Hongxia. Convergence of Perry and Shanno's memoryless quassi-Newton method for nonconvex optimization problems [J]. 运筹学学报, 1997, 1(1): 22-28.

[9] 谢铁军, 陈明文, 程涛. 带有参数的 Perry-Shanno 无记忆拟牛顿方法的收敛性 [J]. 北京科技大学学报, 2000, 22(6): 16-18.

[10] 谢铁军, 陈明文, 刘任平. 无记忆拟牛顿方法的收敛性 [J]. 运筹与管理, 2000, 9(4): 57-61.

[11] 于静静, 焦宝聪. Perry-Shanno 无记忆拟牛顿法在非单调搜索下的收敛性 [J]. 首都师范大学学报(自然科学版}), 2007, 27(6): 10-14.

[12] 黄亮, 陈忠, 谷军. 基于非单调线搜索的无记忆拟牛顿法的全局收敛性 [J]. 四川理工学院学报(自然科学版}), 2008, 21(3): 7-8.

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Convergence of nonmonotonic Perry-Shanno's memoryless quasi-Newton method with parameters

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