解无约束优化问题的一个新的非单调信赖域算法A New Non-monotone Trust Region Algorithm for Solving Unconstrained Optimization Problems
刘景辉;马昌凤;
摘要(Abstract):
在传统信赖域方法的基础上,提出了求解无约束最优化问题的一个新的带非单调线搜索的信赖域算法.该算法采用非单调Wolfe线搜索技术获得迭代步长,新算法在每一迭代步只需求解一次信赖域子问题,克服了每次迭代求解信赖域子问题时计算量较大的缺点.在一定条件下,证明了算法的全局收敛性.数值实验结果表明该算法是有效的.
关键词(KeyWords): 无约束优化问题;信赖域方法;非单调线搜索;全局收敛性
基金项目(Foundation): 国家自然科学基金资助项目(11071041)
作者(Authors): 刘景辉;马昌凤;
参考文献(References):
- [1]Nocedal J,Yuan Y X.Combining trust region and line search techniques[J].Advances in Nonlinear Program-ming,1998(4):153-175.
- [2]Michael Gertz E.A quasi-Newton trust-region method[J].Mathematical Programming,2004,100(3):447-470.
- [3]Deng N Y,Xiao Y,Zhou F J.A nonmonotonic trust region algorithm[J].Journal of Optimization Theory andApplications,1993,76(2):259-285.
- [4]刘培培,陈兰平.一类拟牛顿非单调信赖域算法及其收敛性[J].数学进展,2008,37(1):92-100.
- [5]Mo Jiangtao,Liu Chunyan,Yan Shicui.A nonmonotone trust region method based on nonincreasing techique ofweighted average of the successive function values[J].Journal of Computational and Applied Mathematics,2007(209):97-108.
- [6]庞善民,陈兰平.一类带非单调线搜索的信赖域算法[J].计算数学,2011,33(1):48-56.
- [7]Zhang H C,Hager W W.A nonmonotone line search technique and its application to unconstrained optimization[J].SIAM J Optim,2004,14(4):1043-1056.
- [8]袁功林,韦增欣.一个新的BFGS信赖域算法[J].广西科学,2004,11(3):195-196.
- [9]马昌凤.最优化方法及其Matlab程序设计[M].北京:科学出版社,2010:72-85.
- [10]Grippo L,Lampariello F,Lucidi S.A nonmonotone line search technique for Newton's method[J].SIAM JNumer Anal,1986,23(4):707-716.
- [11]袁亚湘,孙文瑜.最优化理论与方法[M].北京:科学出版社,1997:154-166.
- [12]Jorge J More,Burton S Garbow,Kenneth E Hillstrom.Testing unconstrained optimization software[J].ACMTransactions on Mathematical Software,1981,7(1):17-41.