| 引用本文： |
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韦增欣,谢品杰,顾能柱.一类拟牛顿算法的收敛性[J].广西科学,2006,13(4):282-287,292. [点击复制]
- WEI Zeng-xin,XIE Pin-jie,GU Neng-zhu.Convergence Properties of a Class of Quasi-Newton Algorithm[J].Guangxi Sciences,2006,13(4):282-287,292. [点击复制]
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| 摘要: |
| 根据一类基于新拟牛顿方程Bk+1sk=yk*的修改BFGS类算法,采用广义Wolfe线搜索模型(GW搜索模型):f(xk+1)≤ f(xk)+δαkgkTdk和g(xk+1)Tdk≥max{,σ,1-(αk‖dk‖)p}gkTdk,其中0<δ≤σ<1,p∈(-∞,1),得到一类修正的BFGS算法(MBFGS),证明了MBFGS算法的全局收敛性和超线性收敛性.数值试验结果表明MBFGS算法是有效的. |
| 关键词: 无约束优化 BFGS算法 全局收敛性 超线性收敛性 |
| DOI： |
| 投稿时间：2006-06-14 |
| 基金项目:国家自然科学基金(No.10161002);广西自然科学基金项目(No.0135004)资助 |
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| Convergence Properties of a Class of Quasi-Newton Algorithm |
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WEI Zeng-xin, XIE Pin-jie, GU Neng-zhu
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| (Department of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, China) |
| Abstract: |
| In this paper,we present a modified BFGS method,which satisfies the quasi-Newton funtion proposed by Wei[11].Under suitable conditions,we establish global convergence and superlinear convergence for our algorithm with the general Wolfe line search.The numerical results are also presented,which show that the proposed algorithm is efficient for unconstrained optimization problems. |
| Key words: unconstrained optimization BFGS method global convergence superlinear convergence |
