Global convergence of a new conjugate gradient method for modified Liu-Storey formula
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摘要: 在 Liu-Storey(LS)公式的基础上给出了一个修正的共轭梯度公式 beta _k^MLS. 证明了该新公式在 Wolfe-Powell 线搜索下, 甚至在强 Wolfe-Powell 线搜索下, 在满足sigma in bigg(0,textstyle1 over 2bigg) 的同时, 新算法具有充分下降性和全局收敛性. 数值结果展现了算法的可行性.Abstract: In this paper, a modified conjugate gradient formula beta _k^MLSbased on the formula of the Liu-Storey(LS) nonlinear conjugate gradient method was proposed. It was proved that under the Wolfe-Powell line search and even under the strong Wolfe-Powell line search, with parameter sigma in bigg(0,frac12bigg), the new method has sufficient descent and global convergence properties. Preliminary numerical results show that the method is very promising.
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