Abstract: An adaptive filter trust region method for large scale unconstrained optimization is proposed.This new algorithm uses the function and its gradients to determine a scale matrix as an approximation of its Hessian matrix in the subproblem.The adaptive technique and filter technique are introduced to improve the behavior of the method.The new algorithm is shown to be globally convergent and numerical experiments indicate that it is very effective for large scale unconstrained minimization problems.

Key words: large scale unconstrained optimization, filter technique, gradient method, adaptive trust region method, global convergence

摘要： 提出一种解大规模无约束优化问题的自适应过滤信赖域法。用目标函数的梯度及迭代点的信息来构造目标函数海赛矩阵的近似数量矩阵，引进了过滤技术和自适应技术，大大提高了计算效率。从理论上证明了新算法的全局收敛性，数值试验结果也表明了新算法的有效性。

关键词: 大规模无约束优化, 过滤技术, 梯度法, 自适应信赖域法, 全局收敛性