| 大规模无约束优化的一族LBFGS类算法 |
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| 引用本文： | 钱小燕,施庆生,刘浩,石岿然. 大规模无约束优化的一族LBFGS类算法[J]. 运筹学学报, 2011, 15(3) |
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| 作者姓名： | 钱小燕 施庆生 刘浩 石岿然 |
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| 作者单位： | 1. 南京工业大学理学院,南京,210009
2. 南京工业大学经济与管理学院,南京21009 |
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| 基金项目： | the National Natural Science Foundation of China(71071075); the Natural Science Project of Nanjing University of Technology(39704017) |
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| 摘 要： | 尝试在有限存储类算法中利用目标函数值所提供的信息.首先利用插值条件构造了一个新的二次函数逼近目标函数,得到了一个新的弱割线方程,然后将此弱割线方程与袁[1]的弱割线方程相结合,给出了一族包括标准LBFGS的有限存储BFGS类算法,证明了这族算法的收敛性.从标准试验函数库CUTE中选择试验函数进行了数值试验,试验结果表明这族算法的数值表现都与标准LBFGS类似.
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| 关 键 词： | 无约束优化 弱割线方程 BFGS算法 收敛性分析 有限存储 |
A Class of LBFGS-Type Algorithms for Large-Scale Unconstrained Optimization |
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| QIAN Xiaoyan,SHI Qingsheng,LIU Hao,SHI Kuiran. A Class of LBFGS-Type Algorithms for Large-Scale Unconstrained Optimization[J]. OR Transactions, 2011, 15(3) |
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| Authors: | QIAN Xiaoyan SHI Qingsheng LIU Hao SHI Kuiran |
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| Affiliation: | QIAN Xiaoyan SHI Qingsheng LIU Hao SHI Kuiran 1.College of Sciences,Nanjing University of Technology,Nanjing 210009,China 2.College of Economics and Management Science,China |
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| Abstract: | In this paper,value information of objective function is exploited in limited memory BFGS-type algorithms.We first construct a new quadratic function satisfying some interpolation conditions to approximate the objective function,and get a new weak secant equation.Combining the new weak secant equation with that obtained by Yuan[1],a class of limited memory BFGS-type algorithms including the classic LBFGS algorithm based on a new weak secant equation is proposed.The convergence of this class limited memory BFGS-type algorithms is proved.Numerical results for standard test problems from CUTE are reported,which indicate that all the algorithms in the proposed class perform quite well. |
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| Keywords: | unconstrained optimization weak secant equation BFGS algorithm convergence analysis limited memory |
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