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...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.展开更多
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)。
文摘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.
