期刊
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
卷 37, 期 1, 页码 166-175出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s10255-021-0997-9
关键词
Barzilai-Borwein method; trust region method; nonmonotone technique; Metropolis criterion; global convergence
资金
- National Natural Science Foundation of China [12071398, 11671125, 11571074, 61977017]
- Natural Science Foundation of Hunan Province [2020JJ4567]
- Key Scientific Research Found of Hunan Education Department [20A097]
A new nonmonotone trust region BB method is proposed in this paper, which combines 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 and accepts some bad solutions based on the modified Metropolis criterion. Preliminary numerical results show that the new method is more efficient compared to the existing trust region BB method.
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.
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