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.

中文翻译：

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一种新的无约束优化问题的非单调信任域 Barzilai-Borwein 方法

在本文中，我们提出了一种新的非单调信任域 Barzilai-Borwein（简称 BB）方法来解决无约束优化问题。所提出的方法是通过改进的 Metropolis 准则、BB 步长和信任区域方法的新颖组合给出的。新方法利用BB-stepsize的倒数来逼近信任域子问题中目标函数的Hessian矩阵，并根据基于模拟退火思想的修正Metropolis准则接受一些坏解。在一些合适的假设下，新方法的全局收敛性成立。一些初步的数值结果表明，与现有的信任域BB方法相比，新方法更有效。