非单调广义对角拟牛顿算法
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摘要
本文研究了无约束最优化的求解问题.利用新的对角拟牛顿校正和非单调技术,获得了一种非单调广义对角拟牛顿算法.新算法具有低存储、低计算量的特点,非常适合大规模问题的求解,推广了文献[8]的结果.
In this paper, the method for solving unconstrained optimization is studied.By using the new diagonal quasi-Newton update and nonmonotone technique, a nonmonotone generalized diagonal quasi-Newton algorithm is proposed. The new method needs less memory capacitance and computational complexity. It is very effective and attractive for large scale unconstrained problems and generalizes the results of reference [8].
In this paper, the method for solving unconstrained optimization is studied.By using the new diagonal quasi-Newton update and nonmonotone technique, a nonmonotone generalized diagonal quasi-Newton algorithm is proposed. The new method needs less memory capacitance and computational complexity. It is very effective and attractive for large scale unconstrained problems and generalizes the results of reference [8].
引文
[1]Grippo L,Lampariello F,Lucidi S.A nonmonotone line search technique for Newton’s method[J].SIAM J.Numer.Anal.,1986,23(4):707–716.
[2]Deng N Y,Xiao Y,Zhou F J.Nonmontonic trust region algorithm[J].J.Optim.Theory Appl.,1993,76(2):259–285.
[3]Zhang H C,Hager W W.A nonmonotone line search technique and its application to unconstrained optimization[J].SIAM J.Optim.,2004,14(4):1043–1056.
[4]Mo J,Liu C,Yan S.A nonmonotone trust region method based on nonincreasing technique of weighted average of the successive function values[J].J.Comput.Appl.Math.,2007,209(1):97–108.
[5]Gu N,Mo J.Incorporating nonmonotone strategies into the trust region method for unconstrained optimization[J].Comput.Math.Appl.,2008,55(9):2158–2172.
[6]Barzilai J,Borwein J M.Two point step size gradient method[J].IMA J.Numer.Anal.,1988,8(1):141–148.
[7]Raydan M.The Barzilai and Barwein gradient method for large scale unconstrained minimization problem[J].SIAM J.Optim.,1997,7(1):26–33.
[8]时贞军,孙国.无约束优化问题的对角稀疏拟牛顿算法[J].系统科学与数学,2006,26(1):101–112.
[9]孙清滢,刘丽敏,王宣战.修正Grippo非单调线搜索规则的新对角稀疏拟牛顿算法[J].高等学校计算数学学报,2011,33(3):203–214.
[10]孙清滢,郑艳梅.大步长非单调线搜索规则的Lampariello修正稀疏拟牛顿算法的全局收敛性[J].数学进展,2008,37(3):311–320.
[11]Yuan Y.A modified BFGS algorithm for unconstrained optimization[J].IMA J.Numer.Anal.,1991,11(3):325–332.
[12]Zhang J,Xu C.Properties and numerical performance of quasi-Newton methods with modifies quasi-Newton equations[J].J.Comput.Appl.Math.,2001,137(2):269–278.
[13]Wei Z X,Li G Y,Qi L Q.New quasi-Newton methods for unconstrained optimization[J].Appl.Math.Comput.,2006,175(2):1156–1188.
[14]Zhu M,Nazareth J L,Wolkowicz H.The quasi-Cauchy and diagonal updating[J].SIAM J.Optim.,1999,9(4):1192–1204.
[15]Andrei N.An unconstrained optimization test functions collection[J].Adv.Model.Optim.,2008,10(1):147–161.
[16]Dolan E D,Mor′e J J.Benchmarking optimization software with performance profiles[J].Math.Program.,2002,91(2):201–213.
[2]Deng N Y,Xiao Y,Zhou F J.Nonmontonic trust region algorithm[J].J.Optim.Theory Appl.,1993,76(2):259–285.
[3]Zhang H C,Hager W W.A nonmonotone line search technique and its application to unconstrained optimization[J].SIAM J.Optim.,2004,14(4):1043–1056.
[4]Mo J,Liu C,Yan S.A nonmonotone trust region method based on nonincreasing technique of weighted average of the successive function values[J].J.Comput.Appl.Math.,2007,209(1):97–108.
[5]Gu N,Mo J.Incorporating nonmonotone strategies into the trust region method for unconstrained optimization[J].Comput.Math.Appl.,2008,55(9):2158–2172.
[6]Barzilai J,Borwein J M.Two point step size gradient method[J].IMA J.Numer.Anal.,1988,8(1):141–148.
[7]Raydan M.The Barzilai and Barwein gradient method for large scale unconstrained minimization problem[J].SIAM J.Optim.,1997,7(1):26–33.
[8]时贞军,孙国.无约束优化问题的对角稀疏拟牛顿算法[J].系统科学与数学,2006,26(1):101–112.
[9]孙清滢,刘丽敏,王宣战.修正Grippo非单调线搜索规则的新对角稀疏拟牛顿算法[J].高等学校计算数学学报,2011,33(3):203–214.
[10]孙清滢,郑艳梅.大步长非单调线搜索规则的Lampariello修正稀疏拟牛顿算法的全局收敛性[J].数学进展,2008,37(3):311–320.
[11]Yuan Y.A modified BFGS algorithm for unconstrained optimization[J].IMA J.Numer.Anal.,1991,11(3):325–332.
[12]Zhang J,Xu C.Properties and numerical performance of quasi-Newton methods with modifies quasi-Newton equations[J].J.Comput.Appl.Math.,2001,137(2):269–278.
[13]Wei Z X,Li G Y,Qi L Q.New quasi-Newton methods for unconstrained optimization[J].Appl.Math.Comput.,2006,175(2):1156–1188.
[14]Zhu M,Nazareth J L,Wolkowicz H.The quasi-Cauchy and diagonal updating[J].SIAM J.Optim.,1999,9(4):1192–1204.
[15]Andrei N.An unconstrained optimization test functions collection[J].Adv.Model.Optim.,2008,10(1):147–161.
[16]Dolan E D,Mor′e J J.Benchmarking optimization software with performance profiles[J].Math.Program.,2002,91(2):201–213.