| 无约束最优化的一个修正的类BFGS算法 |
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| 引用本文： | 钱小燕. 无约束最优化的一个修正的类BFGS算法[J]. 应用数学, 2011, 24(3) |
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| 作者姓名： | 钱小燕 |
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| 作者单位： | 南京工业大学理学院,江苏南京,210009 |
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| 基金项目： | Supported by the National Natural Science Foundation of China(71071075); the Natural Science Project of Nanjing University of Technology(39704017) |
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| 摘 要： | 利用前一步得到的曲率信息代替xk到xk+1段二次模型的曲率给出一个具有和BFGS类似的收敛性质的类BFGS算法,并揭示新算法与自调比拟牛顿法的关系.从试验函数库CUTE中选择标准试验函数,对比标准BFGS算法及其它改进BFGS算法进行数值试验.试验结果表明这个新算法的表现有点象自调比拟牛顿算法.
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| 关 键 词： | 无约束最优化 拟牛顿法 BFGS 自调比拟牛顿法 修正拟牛顿法 |
A Modified BFGS-type Algorithm for Unconstrained Optimization |
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| QIAN Xiaoyan. A Modified BFGS-type Algorithm for Unconstrained Optimization[J]. Mathematica Applicata, 2011, 24(3) |
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| Authors: | QIAN Xiaoyan |
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| Affiliation: | QIAN Xiaoyan(College of Sciences,Nanjing University of Technology,Nanjing210009,China) |
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| Abstract: | A modified BFGS-type algorithmis proposed,where the current average curvature betweenline segmentxktoxk+1is approxi mated by the nearest past iteration.The algorithmpreserves the convergence properties of the famous BFGS algorithm.The relation between the newalgorithm and a self-scaling quasi-Newton algorithmis revealed.Compared with the classic BFGS and other modified BFGS algorithms,numerical results for standard test problems from CUTEare presented,whichindicate that the numerical performance of the newa... |
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| Keywords: | Unconstrained optimization Quasi-Newton algorithms BFGSalgorithm Self-scaling quasi-Newton algorithm Modified BFGS algorithms |
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