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

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