一个解界约束非线性方程组的无导数回溯线搜索仿射内点信赖域方法（英文）

A Derivative-Free Affine Scaling Trust-Region Method with Interior Backtracking Technique for Bound-Constrained Nonlinear Systems

文章给出了一个求解界约束非线性方程组的无导数回溯线搜索仿射内点信赖域方法.该方法利用非线性方程组的特点,对方程组中每一个函数建立插值模型.通过利用信赖域模型和回溯先搜索技术的结合,利用插值信赖域子问题子问题求解搜索方向,并利用回溯先搜索技术保证可行性.在合理的假设条件下,证明了算法的全局和快速局部收敛性.并且,通过数值实验表明该种无导数算法对求解界约束非线性方程组问题是有效的.

In this paper, a derivative-free affine scaling trust-region method with interior backtracking line search technique is considered for solving bound-constrained nonlinear equations. The proposed algorithm is designed to take advantage of the problem structured by building polynomial interpolation models for each function of nonlinear systems subjective to the bound constraints on variables. By using both trust-region strategy and interior backtracking line search technique, each iterate switches to backtracking step generated by the general derivative-free subproblem and satisfies strict interior point feasibility by line search backtracking technique. Under reasonable conditions, global convergence and fast local convergence rate ofthe algorithm are established. The results of numerical experiments are reported to show the effectiveness of the proposed algorithms.