一个求解非线性方程组和最小二乘问题的过滤集无导数信赖域方法（英文）

作者：陈俊; 陈艳男^*; 孙海琳; 孙文瑜

来源：高等学校计算数学学报, 2021, 43(04): 377-402.

We apply the filter technique to the model-based derivative-free trust region algorithm for solving nonlinear equations and nonlinear least-squares problems.Following the work of Zhang et al.[SIAM J.Optim.,20(2010),pp.3555-3576],we consider building the individual interpolation model for each component function in the nonlinear equations.A multidimensional filter,which is a list of n-tuples,is designed to potentially accept the trial point as the new iterate more often.As far as we know,this is the first work to embed the filter mechanism into the model-based derivative-free optimization.Under suitable conditions,we establish the liminf-type and lim-type first-order global convergence results of the algorithm.Numerical experiments show that the new algorithm is efficient.

• 出版日期2021
• 单位华南师范大学; 南京师范大学; 南京晓庄学院