解大规模非线性方程组的一种三项型投影算法

A Three-term Projection Method for a Large Scale Nonlinear Equations

为加快非线性单调方程组的运算效率,基于高效率线搜索方法和投影技术,构建了一个新型的无导数型三项共轭梯度投影算法.通过改进搜索方向,使得新算法在任何线搜索下都自动满足充分下降性条件和信赖域特性.在一定的假设下,新方法具有全局收敛性,初步数值试验结果表明,新算法比同类算法更加高效.

In our report,in order to enhance the computational speed of solving nonlinear monotone equation,based on the effective line search method and projection technique,a new three-term conjugate gradient projection algorithm without derivative was constructed. Because of improving search direction,the algorithm possesses sufficient descent condition and trust region trait under any line search. Under some reasonable assumptions,the new algorithm converges globally,and which is more efficient than some similar algorithms.