A New Nonmonotone Trust Region Barzilai-Borwein Method for Unconstrained Optimization Problems  

作　　者：Xing LI Wen-li DONG Zheng PENG 

机构地区：[1]College of Mathematics and Computer Science,Fuzhou University,Fuzhou 350108,China [2]School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,China

出　　处：《Acta Mathematicae Applicatae Sinica》2021年第1期166-175,共10页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.12071398,11671125,11571074,61977017);the Natural Science Foundation of Hunan Province(No.2020JJ4567);the Key Scientific Research Found of Hunan Education Department(No.20A097)。

摘　　要：In this paper,we propose a new nonmonotone trust region Barzilai-Borwein(BB for short)method for solving unconstrained optimization problems.The proposed method is given by a novel combination of a modified Metropolis criterion,BB-stepsize and trust region method.The new method uses the reciprocal of BB-stepsize to approximate the Hessian matrix of the objective function in the trust region subproblems,and accepts some bad solutions according to the modified Metropolis criterion based on simulated annealing idea.Under some suitable assumptions,the global convergence of the new method is established.Some preliminary numerical results indicate that,the new method is more efficient compared with the existing trust region BB method.

关 键 词：Barzilai-Borwein method trust region method nonmonotone technique Metropolis criterion global convergence 

分 类 号：O224[理学—运筹学与控制论]