计算数学
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计算数学  2012, Vol. 34 Issue (3): 297-308    DOI:
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一类新型DL共轭梯度法研究
邓松海, 万中
中南大学数学与统计学院, 长沙 410083
A NEW DL-TYPE CONJUGATE GRADIENT METHOD FOR NONCONVEX UNCONSTRAINED OPTIMIZATION PROBLEMS
Deng Songhai, Wan Zhong
School of Mathematics and Statistics, Central South University, Changsha 410083, China
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摘要 提出了求解无约束优化问题的新型DL共轭梯度方法. 同已有方法不同之处在于,该方法构造了一种修正的Armijo线搜索规则,它不仅能给出当前迭代步步长, 而且还能同时确定计算下一步搜索方向时需要用到的共轭参数值. 在较弱的条件下, 建立了算法的全局收敛性理论. 数值试验表明,新型共轭梯度算法比同类方法具有更好的计算效率.
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关键词无约束规划   共轭梯度   全局收敛   非精确线性搜索   下降算法     
Abstract: In this paper, a new DL-type conjugate gradient method is proposed for solving nonconvex unconstrained optimization problems. Different from the existent ones, a new modified Armijo-type line search rule is constructed to give both the steplength and the conjugated parameter being used to determine a search direction in the mean time at each iteration. Under weak conditions, the global convergence of the developed algorithm is established. Numerical experiments show the efficiency of the algorithm, particularly in comparison with the similar ones available in the literature.
Key wordsunconstrained optimization   conjugate gradient   global convergence   inexact line search   descent algorithm   
收稿日期: 2012-02-22;
基金资助:

国家自然科学基金资助(基金号: 71071162, 70921001).

通讯作者: 万中     E-mail: wanmath@163.com
引用本文:   
. 一类新型DL共轭梯度法研究[J]. 计算数学, 2012, 34(3): 297-308.
. A NEW DL-TYPE CONJUGATE GRADIENT METHOD FOR NONCONVEX UNCONSTRAINED OPTIMIZATION PROBLEMS[J]. Mathematica Numerica Sinica, 2012, 34(3): 297-308.
 
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