求解无约束优化问题的新谱共轭梯度法及其收敛性
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引用本文:林穗华.求解无约束优化问题的新谱共轭梯度法及其收敛性[J].经济数学,2013,(4):33-37
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作者单位
林穗华 (广西民族师范学院 数学与计算机科学系广西 崇左 532200) 
中文摘要:强Wolfe条件不能保证标准CD共轭梯度法全局收敛.本文通过建立新的共轭参数,提出无约束优化问题的一个新谱共轭梯度法,该方法在精确线搜索下与标准CD共轭梯度法等价,在标准Wolfe线搜索下具有下降性和全局收敛性.初步的数值实验结果表明新方法是有效的,适合于求解非线性无约束优化问题.
中文关键词:无约束优化  谱共轭梯度法  下降性  全局收敛
 
A New Spectral Conjugate Gradient Method for Unconstrained Optimization and Its Convergence
Abstract:Strong Wolfe line search conditions cannot guarantee the global convergence of standard CD conjugate gradient method.A new spectral conjugate gradient method for unconstrained optimization was proposed.This method is the same as the standard CD method when the line search is exact.Moreover, the corresponding algorithm was proved to be descent and globally convergent if the Wolfe line search is used.Preliminary numerical results show that the new method is efficent, suitable for solving nonlinear unconstrained optimization problems.
keywords:unconstrained optimization  spectral conjugate gradient method  descent property  global convergence
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