Armijo型线搜索下一个修正Hestenes-Stiefel共轭梯度法的全局收敛性

Global Convergence of a Modified Hestenes-Stiefel Conjugate Gradient Method under Armijo-type Line Search

摘要: 提出一个新的修正Hestenes-Stiefel(HS)非线性共轭梯度法(MHSCG算法)．在精确线搜索下MHSCG算法化归为标准的HS共轭梯度算法．该算法产生的搜索方向不依赖于线搜索准则而具有充分下降性．新方法在一个修正Armijo型线搜索下具有全局收敛性．数值试验表明,对于多数算例新算法比PRP、HS、LS算法具有更好的计算结果．

Abstract: A new modified Hestenes-Stiefel nonlinear conjugated gradient (MHSCG) algorithm was put forth. Under exact line search the new algorithm is standardized as an HS algorithm. The new algorithm characterized by its independence of the line search rules and a sufficient descent property under Armijo line search and is of good global convergence. Preliminary numerical results show that the method gives a better performance in contrast with algorithms like PRP, HS and LS.