Wolfe线搜索下一类混合共轭梯度法的全局收敛性

摘要

In this paper, a new conjugate gradient formula is presented. The new formula is the same as DY formula when the line search is exact. Some properties of the new formula are discussed. We propose a new conjugate gradient algorithm for unconstrained optimization with a mixed formula that combines the new formula and DY formula. The algorithm produces a descent direction. The global convergence of the algorithm is proved, some numerical examples are given.%本文给出了一个新的共轭梯度公式,新公式在精确线搜索下与DY公式等价,并给出了新公式的相关性质.结合新公式和DY公式提出了一个新的混合共轭梯度法,新算法在Wolfe线搜索下产生一个下降方向,并证明了算法的全局收敛性,并给出了数值例子.