菏泽学院学报

以线性规划为基础的非单调信赖域算法，试探步长求解过程过于复杂，使得算法迭代次数过多.因此，提出基于非线性方程组的非单调信赖域算法研究.依托于凝聚函数，完成最优化问题与非线性方程组问题之间的转换.运用Hessian矩阵和双割线折线算法，简化信赖域试探步长求解模式，构建以非线性方程组为基础的非单调信赖域算法.再建立一个多维过滤集，对求解出的试探步长进行判断，求解出最优试探步长.最后，对非单调信赖域算法的全局收敛性质进行验证，保证算法收敛性符合要求后，完成非单调信赖域算法研究.数值实验结果表明：所提算法与ANIR算法、MNMTRLS算法相比，迭代次数减少了40%、57%,有效提升了算法迭代性能.

The non-monotonic trust region algorithm based on linear programming has too many iterations because of the complexity of the solution process of the trial step. Therefore, this paper proposes a non-monotonic trust region algorithm based on nonlinear equations. Based on the condensation function, this algorithm completes the transformation between optimization problems and nonlinear equations. By using Hessian matrix and double secant broken line algorithm, the trial step size solution mode of trust region is simplified, and a non-monotonic trust region algorithm based on nonlinear equations is constructed. Then, a multi-dimensional filter set is established to determine the optimal trial step size. Finally, the global convergence property of the non-monotonic trust region algorithm is verified to ensure that the convergence meets the requirements. The numerical results show that compared with ANIR algorithm and MNMTRLS algorithm, the iteration times of the proposed algorithm are reduced by 40% and 57%, respectively, and the iteration performance of the algorithm is effectively improved.