二次插值模型直接搜索算法的参数分析  

SENSITIVITY OF PARAMETERS IN DIRECT SEARCH METHODS BASED ON QUADRATIC INTERPOLATION MODEL

作　　者：刘浩[1,2] 倪勤[3] 

机构地区：[1]南京航空航天大学经济管理学院,南京210016 [2]南京工业大学理学院,南京210009 [3]南京航空航天大学理学院,南京210016

出　　处：《数值计算与计算机应用》2008年第4期267-276,共10页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(10471062);江苏省基础研究计划(自然科学基金BK2006184)资助项目.

摘　　要：对无约束优化问题的二次插值型直接搜索算法中初始插值半径,信赖域初始半径,位移接受准则和信赖域半径调节参数进行了数值实验分析.数值实验表明解无约束优化的基于二次函数插值型的直接搜索算法对初始插值半径和信赖域初始半径比较敏感,对位移接受准则和半径调节参数不敏感.根据数值实验结果推荐初始插值半径的选取应与信赖域初始半径相等,同时给出了基于二次插值型的直接搜索算法中初始插值半径与信赖域初始半径的选择区间和其它参数的推荐值.这些结果对这类算法的数值实现和工程应用是有益的.The sensitivity of parameters in direct search algorithm with quadratic interpolation model is examined by numerical experiments. These parameters are related to the initial radius, the step acceptance and the update of the trust region. According to numerical experiments, it is shown that the numerical efficiency of the direct search algorithm is very sensitive to the initial radius, and is insensitive to the parameters related to the step ac- ceptance and the update of the trust region. Numerical tests show that initial interpolation radius should be equal to initial trust region radius. Recommended ranges of values for initial radius and the values of other parameters are exhibited on the basis of extensive numerical tests, which is beneficial to the implementation of the algorithm and engineering application.

关 键 词：无约束最优化 直接搜索算法 二次插值模型 信赖域 参数分析 

分 类 号：O224[理学—运筹学与控制论]