一类非单调信赖域算法

给出无约束最优化的一类非单调信赖域算法.该算法是对赵英良提出的算法的改进和推广.为了提高这类算法的迭代速度,本文中在rk<0时放大了fl(k)的取值范围.这样可以更快的迭代到rk>0.从而放宽了算法的整体约束条件.另外,赵英良提出的算法在‖δ(k)‖≤σ‖g(k)‖成立的条件下证明了算法的全局收敛性和超线性收敛速度.本文试图去掉此约束条件仍得到算法的全局收敛性及其超线性收敛速度,从而推广了非单调信赖域方法的应用范围.

A Nonmonotonic Trust Region Algorithm

A nonmonotonic trust region algorithm of unconstrained optimization is given in the paper,and this algorithm is the improvement and the promotion compared to the algorithm which was proposed by Zhao Ying-ling.In this paper,the algorithm enlarges the value scope of fl(k) when rk<0.Then,rk may increase such that the algorithm has a quicker iteration rate.On the other hand,in order to prove its convergence and the rate of convergence,Zhao Ying-liang assumed that ‖δ(k)‖≤σ‖g(k)‖ holds.However,we demonstrate that the algorithm is globally convergent and the rate of convergence is superlinear without the use of the assumption.This may enlarge the applications of nonmonotomic trust region methods.