非单调带参数Perry-Shanno无记忆拟牛顿法的收敛性
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摘要
给出了一种非单调带参数的Perry-Shanno无记忆拟牛顿法,对于目标函数为凸函数,在参数满足适当范围的情况下,证明了算法的全局收敛性.
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.
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.
引文
[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-Sbanno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fJl.四川理工学院学报(自然科学st),2008,21(3):7-8.
[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-Sbanno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fJl.四川理工学院学报(自然科学st),2008,21(3):7-8.