两种非单调信赖域算法的数值比较研究

摘要

This paper is aimed at the comparison between two typical non-monotone trust region algorithms for unconstrained optimization. In theory, they both have good convergence properties. The numerical efficiency of the two non-monotone algorithms is the focus of the comparison. Extensive numerical experiments were conducted, making use of the well-known test problems package by J.J. Mot6 et al. [ ACM Transactions on Mathematical Software, 1981,7（ 1 ） ： 17-41 ]. Then the two algorithms were compared by the performance profiles based on the data obtained from the numerical experiments. The analysis indicates that the numerical efficiency of the algorithm NATR is superior to that of the traditional non-monotone trust region algorithm to a certain extent.%目前求解无约束最优化问题的非单调信赖域算法根据其采用的参考函数值的不同主要有两种：一种是传统的基于最大函数值型，一种是基于函数值加权平均型．理论上该两种算法均具有较好的收敛性质，但关于这两种非单调信赖域算法在实际数值计算效率方面的比较还不充分．为此作者利用国际上广泛采用的无约束优化测试函数包（J．J．More et al．ACM Transactions on Mathematical Software，1981，7（1）：17—41）对这两种方法进行大量的数值试验，并采用剖面分析方法对试验数据进行较全面的分析比较，结果表明基于函数值平均权重的非单调信赖域算法其数值效率在一定程度上优于传统的非单调信赖域算法．