Abstract: This paper presents a nonmonotonic trust region algorithm for unconstrained optimization problems based on a cone model, this algorithm takes advantage of the current iteration point order gradient information in solving the trust region subproblem. A new trust region radius selection mechanism is proposed, and it is compared with the classical trust region methods. At the same time, this paper sets some conditions, the global convergence under the conditions of these assumptions is proved. Experimental results show that the algorithm is effective in solving unconstrained optimization problems based on a cone model, and it expands the trust region algorithm applications.

Key words: trust region algorithms, nonmonotonic strategies, unconstrained optimization, cone model, global convergence

摘要： 提出了非单调信赖域算法求解基于锥模型的无约束优化问题，该算法在求解信赖域子问题时充分利用了当前迭代点的一阶梯度信息。提出了一个新的信赖域半径的选取机制，并和经典的信赖域方法作比较分析。设定了一些条件，在这些假设条件下证明了算法是整体收敛的。数值实验结果表明，该算法对基于锥模型的无约束优化问题的求解是行之有效的，拓展了非单调信赖域算法的应用领域。

关键词: 信赖域算法, 非单调技术, 无约束优化, 锥模型, 全局收敛