A new trust region method for nonlinear equations
A new trust region method for nonlinear equations
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DOI：
10.1007/s001860300302
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发表时间：
2003-11-01
影响因子：
1.2
通讯作者：
Wang, Y
中科院分区：
文献类型：
--
作者：
Zhang, JL;Wang, Y
本文提出了一种新的求解非线性方程组的信赖域方法，该方法在确定信赖域半径时考虑了自然残差的信息。在较弱的条件下证明了算法的全局收敛性。与传统的信赖域方法不同，在局部误差有界的条件下，证明了该方法的超线性收敛性。该条件比传统信赖域方法超线性收敛所需的非退化假设弱。我们还提出了一个近似算法的信赖域子问题。初步的数值实验报告。
In this paper, a new trust region method for the system of nonlinear equations is presented in which the determining of the trust region radius incorporates the information of its natural residual. The global convergence is obtained under mild conditions. Unlike traditional trust region method, the superlinear convergence of the method is proven under the local error bound condition. This condition is weaker than the non-degeneracy assumption which is necessary for superlinear convergence of traditional trust region method. We also propose an approximate algorithm for the trust region subproblem. Preliminary numerical experiments are reported.