一个自动确定信赖域半径的锥模型信赖域方法

A Trust Region Method with Automatic Determination of the Trust Region Radius Based on the Conic Model

自适应信赖域算法由于利用了对算法有重大影响的有关当前迭代点的信息,提高了算法的效率,因此对于无约束最优化问题提出一个锥模型自适应信赖域算法.算法中信赖域半径采用新的自适应修正策略.算法在每步迭代中以R-函数变化的速率、水平向量信息以及当前迭代点的一阶导数信息来修正信赖域半径的大小,使得信赖域半径的修正依据于问题本身,克服传统信赖域算法中没有利用当前迭代点的信息修正信赖域半径的缺点.在一定的条件下简洁地给出了算法的全局收敛性分析.算法丰富了已有的自适应信赖域算法.

In this paper, we propose a self-adaptive trust region method based on the conic model for unconstrained optimization problems. The trust region radius is updated with a new self-adaptive strategy. At every iteration, the trust region radius is updated at the variable rate of R-function, the level vector information and the first order derivative information at the current point, thus the upda- tion of the trust region radius is dependent of the problem itself, which overcomes the shortcoming, that the information at the current point in the traditional trust region algorithms is not applied. The global convergence of the new method is briefly analyzed under mild conditions. The method enriches the existing self-adaptive trust region methods.