共查询到18条相似文献,搜索用时 62 毫秒
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共轭梯度法是一类具有广泛应用的求解大规模无约束优化问题的方法. 提出了一种新的非线性共轭梯度(CG)法,理论分析显示新算法在多种线搜索条件下具有充分下降性. 进一步证明了新CG算法的全局收敛性定理. 最后,进行了大量数值实验,其结果表明与传统的几类CG方法相比,新算法具有更为高效的计算性能. 相似文献
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本文提出了一种新的解无约束优化的共轭梯度算法,分析了算法的收敛性,并对算法进行了数值实验.数值实验的结果表明算法是有效的. 相似文献
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§1.前言 有些实践中的优化问题可以按无约束来处理,而且大量非常有效的约束优化算法都涉及无约束优化方法,因此,无约束优化方法在实用上是很重要的。 考虑下面的二次目标函数F(X)的无约束优化问题: 相似文献
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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. 相似文献
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Conjugate gradient optimization algorithms depend on the search directions.with different choices for the parameters in the search directions.In this note,by combining the nice numerical performance of PR and HS methods with the global convergence property of the class of conjugate gradient methods presented by HU and STOREY(1991),a class of new restarting conjugate gradient methods is presented.Global convergences of the new method with two kinds of common line searches,are proved .Firstly,it is shown that,using reverse modulus of continuity funciton and forcing function,the new method for solving unconstrained optimization can work for a continously differentiable function with Curry-Altman‘s step size rule and a bounded level set .Secondly,by using comparing technique,some general convergence propecties of the new method with other kind of step size rule are established,Numerical experiments show that the new method is efficient by comparing with FR conjugate gradient method. 相似文献
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本文给出了一类具有4个参数的共轭梯度法,并且分析了其中两个子类的方法。证明了在步长满足更一般的Wolfe条件时,这两个子类的方法是下降算法。同时还证明了这两个子类算法的全局收敛性。 相似文献
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A family of scaled conjugate gradient algorithms for large-scale unconstrained minimization is defined. The Perry, the Polak—Ribière
and the Fletcher—Reeves formulae are compared using a spectral scaling derived from Raydan's spectral gradient optimization
method. The best combination of formula, scaling and initial choice of step-length is compared against well known algorithms
using a classical set of problems. An additional comparison involving an ill-conditioned estimation problem in Optics is presented.
Accepted 22 August 2000. Online publication 26 February 2001. 相似文献
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本文通过结合牛顿法与PRP共轭梯度法提出一修正PRP方法,新方法中包含了二阶导数信息,在适当的假设下算法全局收敛,数值算例表明了算法的有效性. 相似文献
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Recently, we propose a nonlinear conjugate gradient method, which produces a descent search direction at every iteration and converges globally provided that the line search satisfies the weak Wolfe conditions. In this paper, we will study methods related to the new nonlinear conjugate gradient method. Specifically, if the size of the scalar
k
with respect to the one in the new method belongs to some interval, then the corresponding methods are proved to be globally convergent; otherwise, we are able to construct a convex quadratic example showing that the methods need not converge. Numerical experiments are made for two combinations of the new method and the Hestenes–Stiefel conjugate gradient method. The initial results show that, one of the hybrid methods is especially efficient for the given test problems. 相似文献
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一个新的无约束优化超记忆梯度算法 总被引:3,自引:0,他引:3
本文提出一种新的无约束优化超记忆梯度算法,算法利用当前点的负梯度和前一点的负梯度的线性组合为搜索方向,以精确线性搜索和Armijo搜索确定步长.在很弱的条件下证明了算法具有全局收敛性和线性收敛速度.因算法中避免了存贮和计算与目标函数相关的矩阵,故适于求解大型无约束优化问题.数值实验表明算法比一般的共轭梯度算法有效. 相似文献
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Songhai Deng Zhong Wan Xiaohong Chen 《Journal of Optimization Theory and Applications》2013,157(3):820-842
In this paper, an improved spectral conjugate gradient algorithm is developed for solving nonconvex unconstrained optimization problems. Different from the existent methods, the spectral and conjugate parameters are chosen such that the obtained search direction is always sufficiently descent as well as being close to the quasi-Newton direction. With these suitable choices, the additional assumption in the method proposed by Andrei on the boundedness of the spectral parameter is removed. Under some mild conditions, global convergence is established. Numerical experiments are employed to demonstrate the efficiency of the algorithm for solving large-scale benchmark test problems, particularly in comparison with the existent state-of-the-art algorithms available in the literature. 相似文献
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在修正PRP共轭梯度法的基础上,提出了求解无约束优化问题的一个充分下降共轭梯度算法,证明了算法在Wolfe线搜索下全局收敛,并用数值实验表明该算法具有较好的数值结果. 相似文献
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Sindhu Narayanan & P. Kaelo 《高等学校计算数学学报(英文版)》2021,14(2):527-539
Conjugate gradient methods are interesting iterative methods that solve
large scale unconstrained optimization problems. A lot of recent research has thus
focussed on developing a number of conjugate gradient methods that are more effective. In this paper, we propose another hybrid conjugate gradient method as a linear
combination of Dai-Yuan (DY) method and the Hestenes-Stiefel (HS) method. The
sufficient descent condition and the global convergence of this method are established using the generalized Wolfe line search conditions. Compared to the other
conjugate gradient methods, the proposed method gives good numerical results and
is effective. 相似文献