A variant spectral-type FR conjugate gradient method and its global convergence

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• 作者：Aiguo Lu ; ^a ; ^{xalag@21cn.com} ; Hongwei Liu^a ; Xiuyun Zheng^a ; Weijie Cong^a
• 关键词：Conjugate gradient method ; FR method ; Wolfe line search ; Armijo-type line search ; Global convergence
• 刊名：Applied Mathematics and Computation
• 出版年：2011
• 出版时间：15 February 2011
• 年：2011
• 卷：217
• 期：12
• 页码：5547-5552
• 全文大小：165 K

文摘

In this paper, we propose a variant FR (VFR) formula and corresponding spectral-type conjugate gradient method (SVFR) such that the direction generated is always a descent direction for the objective function. We also extend to such that and have similar conclusions. Under appropriate conditions, we prove that the proposed method is globally convergent under not only Wolfe line search but also Armijo-type line search. Numerical experiments show the SVFR method performs well.