求解非线性单调方程组的修正三项PRP投影算法

A Modified Three-term PRP Projection Method for Solving Nonlinear Monotone Equations

针对求解大规模非线性单调方程组问题,克服其他算法计算复杂、存储量需求和计算量大等不足,基于经典PRP(Polak-Ribière-Polyak)共轭梯度法,设计了一种新的搜索方向公式,结合单调线搜索技术和投影算法,提出一种修正三项PRP投影算法.新算法具有充分下降性和信赖域特征等优点,在适当的条件下新算法具有全局收敛性.初步数值试验结果表明,新算法对选取的测试问题上是有效的,数值表现总体上优于经典PRP共轭梯度法,适合于求解大规模非线性单调方程组.

In order to solve large-scale nonlinear monotone equations and overcome the shortcomings of other algorithms such as complex calculation,large storage requirement and large calculation amount,a new line search formula was designed based on classical PRP(Polak-Ribière-Polyak)conjugate gradient method,a modified three-term PRP projection algorithm was proposed by combining monotone line search technology and projection algorithm.The new algorithm had the advantages of sufficient descent and trust region characteristics.It possessed the global convergence in the proper conditions.The numerical results show that the new algorithm is effective for the selected test problems,and its numerical performance is generally better than the classical PRP conjugate gradient method,which is suitable for solving large-scale nonlinear monotone equations.