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为解决大规模无约束优化问题,该文结合WYL共轭梯度法和谱共轭梯度法,给出了一种WYL型谱共轭梯度法.在不依赖于任何线搜索的条件下,该方法产生的搜索方向均满足充分下降性,且在强Wolfe线搜索下证明了该方法的全局收敛性.与WYL共轭梯度法的收敛性相比,WYL型谱共轭梯度法推广了线搜索中参数σ的取值范围.最后,相应的数值结果表明了该方法是有效的. 相似文献
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针对共轭梯度法求解无约束二次凸规划时,在构造共轭方向上的局限性,对共轭梯度法进行了改进.给出了构造共轭方向的新方法,利用数学归纳法对新方法进行了证明.同时还给出了改进共轭梯度法在应用时的基本计算过程,并对方法的收敛性进行了证明.通过实例求解,说明了在求解二次无约束凸规划时,该方法相比共轭梯度法具有一定的优势. 相似文献
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由William W.Hager和张洪超提出的一种新的共轭梯度法(简称HZ方法),已被证明是一种有效的方法.本文证明了HZ共轭梯度法在Armijo型线性搜索下的全局收敛性.数值实验显示,在Armijo型线性搜索下的HZ共轭梯度法比在Wolfe线性搜索下更有效. 相似文献
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共轭梯度法是求解无约束优化问题的一种重要的方法.本文提出一族新的共轭梯度法,证明了其在推广的Wolfe非精确线搜索条件下具有全局收敛性.最后对算法进行了数值实验,实验结果验证了该算法的有效性. 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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本文提出了一类与HS方法相关的新的共轭梯度法.在强Wolfe线搜索的条件下,该方法能够保证搜索方向的充分下降性,并且在不需要假设目标函数为凸的情况下,证明了该方法的全局收敛性.同时,给出了这类新共轭梯度法的一种特殊形式,通过调整参数ρ,验证了它对给定测试函数的有效性. 相似文献
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共轭梯度法是求解大规模无约束优化问题最有效的方法之一.对HS共轭梯度法参数公式进行改进,得到了一个新公式,并以新公式建立一个算法框架.在不依赖于任何线搜索条件下,证明了由算法框架产生的迭代方向均满足充分下降条件,且在标准Wolfe线搜索条件下证明了算法的全局收敛性.最后,对新算法进行数值测试,结果表明所改进的方法是有效的. 相似文献
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Sne?ana S.DJORDJEVI? 《数学物理学报(B辑英文版)》2019,(1)
In this paper, we present a new hybrid conjugate gradient algorithm for unconstrained optimization. This method is a convex combination of Liu-Storey conjugate gradient method and Fletcher-Reeves conjugate gradient method. We also prove that the search direction of any hybrid conjugate gradient method, which is a convex combination of two conjugate gradient methods, satisfies the famous D-L conjugacy condition and in the same time accords with the Newton direction with the suitable condition. Furthermore, this property doesn't depend on any line search. Next, we also prove that, moduling the value of the parameter t,the Newton direction condition is equivalent to Dai-Liao conjugacy condition.The strong Wolfe line search conditions are used.The global convergence of this new method is proved.Numerical comparisons show that the present hybrid conjugate gradient algorithm is the efficient one. 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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Saman Babaie-Kafaki 《Optimization Letters》2013,7(4):831-837
Satisfying in the sufficient descent condition is a strength of a conjugate gradient method. Here, it is shown that under the Wolfe line search conditions the search directions generated by the memoryless BFGS conjugate gradient algorithm proposed by Shanno satisfy the sufficient descent condition for uniformly convex functions. 相似文献
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一种混合的HS-DY共轭梯度法 总被引:19,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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P. Armand 《Journal of Optimization Theory and Applications》2007,132(2):287-305
This paper proposes a line search technique to satisfy a relaxed form of the strong Wolfe conditions in order to guarantee
the descent condition at each iteration of the Polak-Ribière-Polyak conjugate gradient algorithm. It is proved that this line
search algorithm preserves the usual convergence properties of any descent algorithm. In particular, it is shown that the
Zoutendijk condition holds under mild assumptions. It is also proved that the resulting conjugate gradient algorithm is convergent
under a strong convexity assumption. For the nonconvex case, a globally convergent modification is proposed. Numerical tests
are presented.
This paper is based on an earlier work presented at the International Symposium on Mathematical Programming in Lausanne in
1997. The author thanks J. C. Gilbert for his advice and M. Albaali for some recent discussions which motivated him to write
this paper. Special thanks to G. Liu, J. Nocedal, and R. Waltz for the availability of the software CG+ and to one of the
referees who indicated to him the paper of Grippo and Lucidi (Ref. 1). 相似文献
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Xiaojing Zhu 《Computational Optimization and Applications》2017,67(1):73-110
In this paper we propose a new Riemannian conjugate gradient method for optimization on the Stiefel manifold. We introduce two novel vector transports associated with the retraction constructed by the Cayley transform. Both of them satisfy the Ring-Wirth nonexpansive condition, which is fundamental for convergence analysis of Riemannian conjugate gradient methods, and one of them is also isometric. It is known that the Ring-Wirth nonexpansive condition does not hold for traditional vector transports as the differentiated retractions of QR and polar decompositions. Practical formulae of the new vector transports for low-rank matrices are obtained. Dai’s nonmonotone conjugate gradient method is generalized to the Riemannian case and global convergence of the new algorithm is established under standard assumptions. Numerical results on a variety of low-rank test problems demonstrate the effectiveness of the new method. 相似文献