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本文我们讨论了一簇共轭梯度法,它可被看作是FR法和DY法的凸组合.我们提出了两种Armijo型线搜索,并在这两种线搜索下,讨论了共轭梯度法簇的全局收敛性. 相似文献
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改进的共轭梯度法及其收敛性 总被引:1,自引:0,他引:1
本文对无约束最优化问题提出一类改进的共轭梯度法。该算法采用一类非精确线搜索,扩大了迭代参数的选取范围,并在目标函数连续可微的条件下,证明了算法的全局收敛性。 相似文献
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限制PR共轭梯度法及其全局收敛性 总被引:5,自引:0,他引:5
PR共轭梯度法是求解大型无约束优化问题的有效算法之一,但是算法的全局收敛性在理论上一直没有得到解决。本文将PR共轭梯度法中的参数β加以限制,提出了限制R共轭梯度法,证明了Armijo搜索下算法的全局收敛性、数值试验表明算法是很有效的。 相似文献
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Yu-hong Dai 《计算数学(英文版)》2001,19(5):539-548
1. IntroductionConsider the unconstrained OPtbo8tion problem,min f(x), (1.1)where j is smooth and its gradient g is available. Conjugate gradieot methods are highly usefulfOr solving (1.1) especially if n is large. They are iterative methods of the formHere oh is a 8tepsbo obtained by a 1-dboensional line search and gk is a scalar. The chOiceof Ph is such tha (l.2)--(l.3) reduces to the linear cOnugate gradient method in the casewhen j is a strictly convex qUadratic and crk is the exact 1-… 相似文献
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一种混合的HS-DY共轭梯度法 总被引:22,自引:3,他引:19
本文在HS方法和DY方法的基础上,综合两者的优势,提出了一种求解无约束优化问题的新的混合共轭梯度法.在Wolfe线搜索下,不需给定下降条件,证明了算法的全局收敛性.数值试验表明,新算法较之HS方法和PR方法更加有效. 相似文献
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A NOTE ON THE NONLINEAR CONJUGATE GRADIENT METHOD 总被引:2,自引:0,他引:2
Yu-hong Dai Ya-xiang Yuan 《计算数学(英文版)》2002,20(6):575-582
The conjugate gradient method for unconstrained optimization problems varies with a scalar. In this note, a general condition concerning the scalar is given, which ensures the global convergence of the method in the case of strong Wolfe line searches. It is also discussed how to use the result to obtain the convergence of the famous Fletcher-Reeves, and Polak-Ribiere-Polyak conjugate gradient methods. That the condition cannot be relaxed in some sense is mentioned. 相似文献
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共轭梯度法是求解无约束最优化问题的有效方法.本文在βkDY的基础上对βk引入参数,提出了一类新共轭梯度法,并证明其在强Wolfe线性搜索条件下具有充分下降性和全局收敛性. 相似文献
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In this paper we consider the global convergence of any conjugate gradient method of the form d1=-g1,dk+1=-gk+1+βkdk(k≥1)with any βk satisfying sume conditions,and with the strong wolfe line search conditions.Under the convex assumption on the objective function,we preve the descenf property and the global convergence of this method. 相似文献
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A new adaptive subspace minimization three-term conjugate gradient algorithm with nonmonotone line search is introduced and analyzed in this paper.The search directions are computed by minimizing a quadratic approximation of the objective function on special subspaces,and we also proposed an adaptive rule for choosing different searching directions at each iteration.We obtain a significant conclusion that the each choice of the search directions satisfies the sufficient descent condition.With the used nonmonotone line search,we prove that the new algorithm is globally convergent for general nonlinear functions under some mild assumptions.Numerical experiments show that the proposed algorithm is promising for the given test problem set. 相似文献
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一种改进的共轭梯度法及全局收敛性 总被引:1,自引:0,他引:1
本文在DY共轭梯度法的基础上对解决无约束最优化问题提出一种改进的共轭梯度法.该方法在Wolfe线搜索下能够保证充分下降性,并在目标函数可微的条件下,证明了算法的全局收敛性.大量数值试验表明,该方法是很有效的. 相似文献