| 曹伟,王开荣,王义利.一种修正的谱CD共轭梯度算法的全局收敛性[J].数学研究及应用,2011,31(2):261~268 |
| 一种修正的谱CD共轭梯度算法的全局收敛性 |
| Global Convergence of a Modified Spectral CD Conjugate Gradient Method |
| 投稿时间：2009-05-12 修订日期：2009-12-08 |
| DOI：10.3770/j.issn:1000-341X.2011.02.009 |
| 中文关键词: 无约束优化 共轭梯度法 Armijo型线搜索 全局收敛性. |
| 英文关键词:unconstrained optimization conjugate gradient method armijo-type line search global convergence. |
| 基金项目:重庆市2010年高等教育教学改革研究重点项目(Grant No.102104). |
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| 中文摘要: |
| 文章在解决大规模无约束优化问题上,提出了一种新非线性修正的谱CD共轭梯度方法.由该方法得到的搜索方向对于目标函数而言是很好的下降方向,这一性质既不受线搜索规则的影响,也不受目标函数的凸性影响.而且该修正的方法在精确线搜索条件下,能诱导出标准的CD共轭梯度方法.在假设条件下,证明了在Armijo型线搜索和Wolfe型线搜索规则下新方法的全局收敛性,初步数值实验结果显示了算法的可行性. |
| 英文摘要: |
| In this paper, we present a new nonlinear modified spectral CD conjugate gradient method for solving large scale unconstrained optimization problems. The direction generated by the method is a descent direction for the objective function, and this property depends neither on the line search rule, nor on the convexity of the objective function. Moreover, the modified method reduces to the standard CD method if line search is exact. Under some mild conditions, we prove that the modified method with line search is globally convergent even if the objective function is nonconvex. Preliminary numerical results show that the proposed method is very promising. |
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