【摘要】 共轭梯度法是求解大规模无约束优化的有效方法之一.该文首先对Hestenes-Stiefel (HS)共轭参数改进,再通过引入重启条件及重启方向,建立两个带重启方向的改进HS型共轭梯度法.第一个方法在弱Wolfe线搜索下产生下降方向,第二个方法独立于任何线搜索得到充分下降性.常规假设下,分析并获得两个新方法的全局收敛性.最后,数值比对试验结果及性能图显示新方法是有效的.更多还原

【Abstract】 The conjugate gradient method is one of the effective methods to solve large-scale unconstrained optimization.In this paper,the Hestenes-Stiefel(HS) conjugate parameter is improved,and then two extended HS-type conjugate gradient methods with restart directions are established by introducing restart conditions and restart directions.The first method produces descent direction under the weak Wolfe line search,and the second one obtains sufficient descent independent of any line search.Under conventional assumptions,the global convergence results of the two proposed methods are analyzed and obtained.Finally,the numerical comparison results and performance graphs show the effectiveness of the new methods.更多还原