求解非光滑方程组的三次正则化方法

A cubic regularization method for solving nonsmooth equations

考虑求解非光滑方程组的三次正则化方法及其收敛性分析.利用信赖域方法的技巧,保证该方法是全局收敛的.在子问题非精确求解和BD正则性条件成立的前提下,分析了非光滑三次正则化方法的局部收敛速度.最后,数值实验结果验证了该算法的有效性.

A cubic regularization method and its convergence for solving a nonsmooth system of equations are studied in this paper.By applying the classical trust region technique,the proposed method is ensured to be globally convergent.When BDregular condition is satisfied and the subproblem is inexactly solved,we analyze the local convergence rate of the nonsmooth cubic regularization method.Finally,the efficiency of our method is verified by numerical results.