A Nonmonotonic Trust Region Algorithm
Ke Ting · Journal of Henan Polytechnic University · 2007
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 rk0.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.