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| 1 | A CLASS OF REVISED BROYDEN ALGORITHMS WITHOUT EXACT LINE SEARCH显示文摘In this paper, we discuss the convergence of the Broyden algorithms with revised search direction. Under some inexact line searches, we prove that the algorithms are globally convergent for continuously differentiable functions and the rate of local convergence of the algorithms is one-step superlinear and n-step second-order for uniformly convex objective functions. | Ding-guoPu Sheng-huaGui Wei-wenTian | 2004 | Journal of Computational Mathematics2004，22，1： | 8 |
| 2 | 带非精确线搜索的调整搜索方向DFP算法(英文)显示文摘本文介绍一类新的带调整搜索方向的Broyden算法.我们着重讨论带调整搜索方向的DFP算法的收敛性,在某些非精确线搜索的情况下,我们证明对连续可微目标函数,这算法是整体收敛的,而对一致凸目标函数,收敛速度是一步超线收敛的.从这篇文章的证明过程中,可以得到对一致凸目标函数,DFP算法具有一步超线形收敛. | 濮定国 王华 田蔚文 | 2004 | 运筹学学报2004，8，3： | 5 |
| 3 | THE CONVERGENCE OF BROYDEN ALGORITHMS FOR LC GRADIENT FUNCTION显示文摘In this paper, we discuss the convergence of Broyden algorithms for the functions which are non-twice differentiable, but have LC gradient. We prove that the rate of convergence of the algorithms is linear for uniformly convex functions. We also demonstrate that under some mild conditions the algorithms are superlinsarly convergent. | 濮定国 | 2000 | Acta Mathematicae Applicatae Sinica2000，16，3： | 1 |
| 4 | A CLASS OF REVISED BROYDEN ALGORITHMS显示文摘In this paper, we discuss the convergence of the Broyden algorithms with revised search direction. Under some inexact llne searches, we prove that the algorithms are globally convergent for continuously differentiable functions and the rate of convergence of the algorithms is one-step superlinear and n-step second-order for uniformly convex objective functions. | PUDingguo TIANWeiwen | 2003 | Journal of Systems Science & Complexity2003，16，2： | 1 |
| 5 | CONVERGENCE PROPERTIES OF DFP METHOD WITH MODIFIED QUASI-NEWTON EQUATIONS显示文摘Quasi-Newton (QN) equation plays a core role in contemporary nonlinear optimization. The traditional QN equation employs only the gradients, but ignores the function value information, which seems unreasonable. In this paper, we consider a class of DFP method with new QN equations which use both gradient and function value infor- mation and ask very little additional computation. We give the condition of convergence and superlinear convergence for these methods. We also prove that under some line search conditions the DFP method with new QN equations is convergeot and superlinearly con- vergent. | TIAN Weiwen (Shanghai University, Shanghai 200436, China) PU Dingguo (Tongji University, Shanghai 200333, China) | 2001 | Journal of Systems Science & Complexity2001，14，3： | 0 |
| 6 | 改进的不带线搜索的两参数簇共轭梯度方法显示文摘不带线搜索的共轭梯度方法即给出步长的具体公式来代替线搜索,由Sun和Zhang[1]首次提出。 Sun 和Cheng[2]证明了不带线搜索的两参数簇共轭梯度方法的全局收敛性。本工作深入了他们的研究;还借用拟牛顿方法的思想,改进了不带线搜索的两参数簇共轭梯度方法,并给出了具体算法和数值结果。从数值结果可以看出,改进的不带线搜索的两参数簇共轭梯度方法是很有效的。 | 李霞 桂胜华 | 2004 | 上海第二工业大学学报2004，21，2： | 0 |
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