一种修正PRP共轭梯度法的全局收敛性  

Global convergence of a modified PRP conjugate gradient method

作　　者：李灿[1] 

机构地区：[1]红河学院数学学院,云南蒙自661199

出　　处：《安徽大学学报（自然科学版）》2013年第2期41-44,共4页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11161020)

摘　　要：PRP共轭梯度法是众多求解无约束优化问题的共轭梯度法中数值效果表现最好的算法之一.提出一种修正的PRP共轭梯度法,该算法始终产生充分下降方向,并且该充分下降性的产生不依赖于任何线搜索.在一定的条件下,证明了该算法在Armijo型线搜索下求解无约束优化问题时具有全局收敛性.最后,给出了相应的数值结果,证明了该算法的有效性.One of the most effective conjugate gradient methods for solving unconstrained optimization problem was PRP conjugate gradient method.In the paper,the author proposed a modified PRP conjugate gradient method.The method generated the descent direction,and the property was independent of the line search used.Furthermore,we proved the global convergence of the method with Armijo-type line search for solving unconstrained optimization problem.At the end of the paper,the author also presented numerical experiment to show the efficiency of the proposed method.

关 键 词：无约束优化问题 PRP共轭梯度法 ARMIJO型线搜索 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]