Global Convergence Properties of Nonlinear Conjugate Gradient Methods with Modified Secant Condition
Global Convergence Properties of Nonlinear Conjugate Gradient Methods with Modified Secant Condition
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DOI：
10.1023/b:coap.0000026885.81997.88
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发表时间：
2004-07
影响因子：
2.2
通讯作者：
H. Yabe;M. Takano
中科院分区：
文献类型：
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作者：
H. Yabe;M. Takano
共轭梯度法对于大规模非线性优化问题很有吸引力。最近，为了期望方法能够快速收敛，Dai和Liao(2001)使用了拟牛顿法的割线条件。在本文中，我们利用了Zhang等人给出的修正割线条件。 (1999) 和Zhang 和Xu (2001) 并继Dai 和Liao (2001) 之后提出了一种新的共轭梯度方法。该方法的新特点是同时利用可用的梯度和函数值信息，在逼近目标函数的二阶曲率时实现了高阶精度。该方法在某些假设下被证明是全局收敛的。报告数值结果。
Conjugate gradient methods are appealing for large scale nonlinear optimization problems. Recently, expecting the fast convergence of the methods, Dai and Liao (2001) used secant condition of quasi-Newton methods. In this paper, we make use of modified secant condition given by Zhang et al. (1999) and Zhang and Xu (2001) and propose a new conjugate gradient method following to Dai and Liao (2001). It is new features that this method takes both available gradient and function value information and achieves a high-order accuracy in approximating the second-order curvature of the objective function. The method is shown to be globally convergent under some assumptions. Numerical results are reported.