一类新的自适应信赖域算法

A New Class Self-adaptive Trust Region Algorithm

提出了一类新的自适应信赖域算法．该算法利用相邻迭代点的实际下降量与预测下降量的比值加权和来衡量二次模型的近似程度，同时信赖域半径迭代准则采用由以．函数给出的一类自适应迭代准则．在一定假设的条件下，算法具有传统信赖域算法的全局收敛性．数值实验表明，算法是稳健和有效的．

This paper presents a nwe class of adaptive trust region algorithm. Ratios about the actual reduction and the predicition reduction around adjacent iteration points are weighted. It measures the approximate extent of the quadratic model and the objective ruction at current iterate point by the weighted sum. The trust region update rules adpot the new self-adaptive update rules introduced by A-function. Under some suitable assumptions, the algorithm has global convergence of the traditional trust region algorithm. Numerical experiments show that the algorithm is robust and effective.