共轭梯度法是求解大规模无约束优化问题的一类重要方法.由于共轭梯度法产生的搜索方向不一定是下降方向,为保证每次迭代方向都是下降方向,本文提出一种求解无约束优化问题的谱共轭梯度算法,该方法的每次搜索方向都是下降方向.当假设目标函数一致凸,且其梯度满足Lipschitz条件,线性搜索满足Wolfe条件时,讨论所设计算法的全局收敛性.
Conjugate gradient methods are class of important methods for unconstrained optimization, especially when the dimension is large. It is well-known that the direction generated by a conjugate gradient method may not be a descent direction. In this paper, we present a spectral conjugate gradient method,which search direction is a descent direction. If the objective function is uniformly convex and its gradient satisfies Lipschitz continuous,the line search satisfies Wolfe condition, the proposed method is shown to be gtohally convergent.