信赖域方法在Hölderian局部误差界下的收敛性质

ON THE CONVERGENCE OF THE TRUST REGION METHOD UNDER THE HÖLDERIAN ERROR BOUND CONDITION

信赖域方法是求解非线性方程组的一种重要方法.本文研究了求解非线性方程组的信赖域半径趋于零的信赖域算法在Jacobi矩阵Hölderian连续条件下的全局收敛性质,以及其在Hölderian局部误差界和Jacobi矩阵Hölderian连续条件下的收敛速度.

The trust region method is an improtant method for solving nonlinear equations.In this paper,we study the global convergence of the trust region method with trust region converging to zero under the Hölderian continuousness of the Jacobian.The convergence rate of the method is also given under the Hölderian error bound condition.