| 一种修正的谱CD共轭梯度算法的全局收敛性 |
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| 引用本文： | 曹伟,王开荣,王义利.一种修正的谱CD共轭梯度算法的全局收敛性[J].数学研究及应用,2011,31(2):261-268. |
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| 作者姓名： | 曹伟 王开荣 王义利 |
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| 作者单位： | 重庆大学数理学院, 重庆 400030;重庆大学数理学院, 重庆 400030;重庆大学数理学院, 重庆 400030 |
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| 基金项目： | 重庆市2010年高等教育教学改革研究重点项目(Grant No.102104). |
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| 摘 要： | In this paper,we present a new nonlinear modified spectral CD conjugate gradient method for solving large scale unconstrained optimization problems.The direction generated by the method is a descent direction for the objective function,and this property depends neither on the line search rule,nor on the convexity of the objective function.Moreover,the modified method reduces to the standard CD method if line search is exact.Under some mild conditions,we prove that the modified method with line search is globally convergent even if the objective function is nonconvex.Preliminary numerical results show that the proposed method is very promising.
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| 关 键 词： | unconstrained optimization conjugate gradient method armijo-type line search global convergence |
| 收稿时间： | 2009/5/12 0:00:00 |
| 修稿时间： | 2009/12/8 0:00:00 |
Global Convergence of a Modified Spectral CD Conjugate Gradient Method |
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| Wei CAO,Kai Rong WANG and Yi Li WANG.Global Convergence of a Modified Spectral CD Conjugate Gradient Method[J].Journal of Mathematical Research with Applications,2011,31(2):261-268. |
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| Authors: | Wei CAO Kai Rong WANG and Yi Li WANG |
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| Institution: | College of Mathematics and Statistics, Chongqing University, Chongqing 401331, P. R. China |
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| Abstract: | In this paper, we present a new nonlinear modified spectral CD conjugate gradient method for solving large scale unconstrained optimization problems. The direction generated by the method is a descent direction for the objective function, and this property depends neither on the line search rule, nor on the convexity of the objective function. Moreover, the modified method reduces to the standard CD method if line search is exact. Under some mild conditions, we prove that the modified method with line search is globally convergent even if the objective function is nonconvex. Preliminary numerical results show that the proposed method is very promising. |
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| Keywords: | unconstrained optimization conjugate gradient method armijo-type line search global convergence |
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