一个全局收敛的改进PRP-HS混合共轭梯度法

A Modified PRP-HS Hybrid Conjugate Gradient Method with Global Convergence

共轭梯度法因其迭代简单,存储量低,成为求解大规模无约束优化的有效方法之一.本文利用著名的PRP和HS方法及其改进版本,提出一个改进PRP-HS混合共轭梯度法,且其共轭参数满足非负性.独立于任何线搜索,新方法每次迭代总产生下降方向.在一般的假设下,使用弱Wolfe线搜索计算步长,可获得新方法的全局收敛性.经大量数值试验并与同类方法作比较,结果表明新方法是有效的.

The conjugate gradient method is one of the most effective methods for solving large-scale unconstrained optimization problems due to its simple structure and low storage capacity. In this paper, using the famous PRP and HS methods and their modified versions, a modified PRP-HS hybrid conjugate gradient method is proposed. The conjugate parameter generated by the proposed method is always nonnegative, and the proposed method can generate descent directions independent of any line search at every iteration. Under general assumptions the global convergence of the proposed method is obtained by using the weak Wolfe line search to calculate step-lengths. A large number of numerical tests and comparisons show that the new method is effective.