一类改进的谱共轭梯度法

A Kind of Improved Spectral Conjugate Gradient Method

谱共轭梯度法是在共轭梯度法基础上发展起来的新型算法,其特点是有两个方向控制参数,是解决大规模无约束优化问题的有效方法,也是优化工作者研究的热点。本文基于已有的非线性谱共轭梯度法提出了一类新的谱共轭梯度法,利用新构造的共轭方向调控参数βk构建了新的算法,并保证了该算法在任何线搜索下都满足共轭条件,进而在迭代时产生的搜索方向都是充分下降的。在Wolfe线搜索下,该方法的全局收敛性得以验证。

The spectral conjugate gradient method is a new algorithm developed on the basis of the conjugate gradient method. Its characteristic is to control parameters in two directions. It is an effective method to solve large-scale unconstrained optimization problems and a hot topic for optimization workers. In this paper, based on the existing nonlinear spectral conjugate gradient method, a new class of spectral conjugate gradient method was proposed. Using the newly constructed conjugate direction control parameter β_(k), a new algorithm was constructed, and it is guaranteed that the algorithm meets the conjugate condition under any line search, and the search direction generated during iteration is fully reduced. Under the Wolfe line search, the global convergence of the method was verified.