解大规模非线性方程组的新型梯度类投影算法

A New Gradient Class Projection Algorithm for Large Scale Nonlinear Equations

针对高效求解大规模非线性单调方程组问题,克服其他算法存储量大等缺点,构建出一个新型的搜索方向,结合线搜索技术和超平面投影方法,提出一种无导数型共轭梯度投影算法。新算法满足以下优点:(1)在不依赖于任何线搜索下,自动满足充分下降性条件;(2)在合理的假设条件下,具有全局收敛性。初步的数值试验结果表明,对于求解大规模非线性单调方程组,在相同条件下新算法比同类算法更高效。

In order to overcome the short comings of some algorithms,such as needs of large storage,a conjugate gradient projection algorithm without derivative for nonlinear monotone equations is presented by constructing a new search direction,combined by using effective line search technique and hyperplane projection method. The new algorithm possesses the advantages that(1)sufficient descent condition is satisfied without any line searches;that(2)under some reasonable assumptions,the algorithm converges globally. Preliminary numerical results show that it is more efficient than the similar algorithms for solving large scale nonlinear monotone equations under the same condition.