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两种有效的非线性共轭梯度算法

刘金魁   

  1. 重庆三峡学院 数学与统计学院, 重庆万州 404100
  • 收稿日期:2013-01-17 出版日期:2013-08-15 发布日期:2013-09-07
  • 基金资助:

    重庆市教委项目(KJ121112)

刘金魁. 两种有效的非线性共轭梯度算法[J]. 计算数学, 2013, 35(3): 286-296.

Liu Jinkui. TWO EFFICIENT NONLINEAR CONJUGATE GRADIENT METHODS[J]. Mathematica Numerica Sinica, 2013, 35(3): 286-296.

TWO EFFICIENT NONLINEAR CONJUGATE GRADIENT METHODS

Liu Jinkui   

  1. School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404100, Chongqing, China
  • Received:2013-01-17 Online:2013-08-15 Published:2013-09-07
根据CG-DESCENT算法[1]的结构和Powell在综述文献[11]中的建议,给出了两种新的求解无约束优化问题的非线性共轭梯度算法. 它们在任意线搜索下都具有充分下降性质, 并在标准Wolfe线搜索下对一般函数能够保证全局收敛性. 通过对CUTEr函数库中部分著名的函数进行试验, 并借助著名的Dolan & Moré[2]评价方法, 展示了新算法的有效性.
By the structure of CG-DESCENT method[1] and Powell's suggestion in[11], two efficient nonlinear conjugate gradient methods are given. The given methods can be guaranteed the sufficient descent property without out any line search, and be proved the global convergence property for the general functions under the standard Wolfe line search. In particular, by the famous evaluation method of Dolan & Moré[2], the numerical results also show that the proposed methods are more efficient by comparing with the famous CG-DESCENT method using a classical set of problems from CUTEr library.

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