局部误差的有界约束非线性方程组的非单调信赖域算法

摘要

本文提供了在没有非奇异假设的条件下,求解有界约束半光滑方程组的投影信赖域算法.基于一个正则化子问题,求得类牛顿步,进而求得投影牛顿步.在合理的假设条件下,证明了算法不仅具有整体收敛性而且保持超线性收敛速率.%In this paper, we propose a projected trust-region algorithm for solving bound-constrained smooth systems of equations. Based on a regularized problem, we obtain the Newton-like step which generates the projected Newton step. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions without nonsingular assumption. A nonmonotonic criterion should bring about speeding up the convergence rate progress in the contours of the merit function with large curvature. Finally, the results of numerical experiments are reported to show the effectiveness of the proposed algorithm.