| 不假定凸性和精确线搜索时DFP算法的收敛性 |
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| 引用本文： | 濮定国,刘美玲.不假定凸性和精确线搜索时DFP算法的收敛性[J].同济大学学报(自然科学版),2013,41(2):289-292. |
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| 作者姓名： | 濮定国 刘美玲 |
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| 作者单位： | 1. 同济大学数学系,上海200092;河南科技大学数学系,河南洛阳471003
2. 上海电机学院数理教学部,上海,201306 |
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| 基金项目： | 国家自然科学基金(10771162,U1135003) |
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| 摘 要： | 对非凸目标函数,Broyden变尺度算法的收敛性是一个没有完全解决的问题.针对DFP修正公式证明在不假定精确线搜索条件下,对光滑的目标函数,当DFP算法得到的点列收敛时,该点列一定趋向于稳定点.指出对于其他Broyden算法结论都是成立的.
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| 关 键 词： | 变尺度算法 收敛性 凸性 不精确线搜索 |
| 收稿时间： | 2011/12/20 0:00:00 |
| 修稿时间： | 2012/11/3 0:00:00 |
Convergence of DFP Algorithms without Convexity and Exact Line Search Assumptions |
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| Pu Ding Guo and Liu Mei Ling.Convergence of DFP Algorithms without Convexity and Exact Line Search Assumptions[J].Journal of Tongji University(Natural Science),2013,41(2):289-292. |
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| Authors: | Pu Ding Guo and Liu Mei Ling |
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| Institution: | Department of Mathematics, Tongji University, Shanghai 200092, China; Department of Mathematics, Henan University of Science and Technology, Luoyang 471003, China;Department of Mathematics and Physics, Shanghai Dianji University, Shanghai 201306, China |
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| Abstract: | The convergence of the Broyden algorithms without convexity and exact line search assumptions is discussed. It is proved that if the objective function is suitably smooth and the DFP algorithm produces a convergence point sequence, then the limit point of the sequence is a critical point of the objective function. We give mainly a proof for the DFP update, then point out that all the results are true for Broyden algorithms by a remark. |
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| Keywords: | Broyden algorithms convergence convexity inexact line search |
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