无约束非线性优化问题的混合LS-CD谱共轭梯度法

A mixed LS-CD spectral conjugate gradient method for uncontrained nonlinear optimization

为寻求收敛性质和数值表现具佳的无约束优化算法,利用共轭梯度法和含有两个方向调控参数的谱共轭梯度法,结合LS方法与CD方法给出混合的共轭参数和相应的谱参数,建立采用标准Wolfe线搜索的谱共轭梯度算法,证明了算法满足下降性和全局收敛性,数值试验显示算法是有效的,适合于求解大型无约束非线性优化问题.研究结果表明:谱共轭梯度法两个参数的适当构造有利于降低算法的收敛条件,增强算法的适用性.

In order to find a good convergence and numerical expression of unconstrained optimization algorithm at the same time, concentrate on conjugate gradient method and spectral conjugate gradient method with two directions regulatory parameters. This paper presents a conjugate parameter with combining the LS method and the CD method and the corresponding spectral parameter. Based on the parameters, a new spectral conjugate gradient algorithm is proposed which uses the standard Wolfe line search, and the descent property and the global convergence of the algorithm are proved. The given numerical results show that the proposed algorithm is efficient and suitable for solving large-scale unconstrained nonlinear optimization problems. The study result indicates that suitable configuration of two parameters of spectral conjugate gradient method helps reduce the convergence conditions, and enhances the applicability of the algorithm.