A modified Hestenes–Stiefel conjugate gradient method with sufficient descent condition and conjugacy condition

• Xiao Liang Dong ^[1] ; Hong Wei Liu ^[1] ; Yu Bo He ^[2] ; Xi Mei Yang ^[3]
  1. [1] Xidian University

     Xidian University

     China

     
  2. [2] Huaihua University

     Huaihua University

     China

     
  3. [3] Henan Normal University

     Henan Normal University

     China

     

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• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 281, Nº 1 (June 2015), 2015, págs. 239-249
• Idioma: inglés
• DOI: 10.1016/j.cam.2014.11.058
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• Resumen

  • In this paper, by taking a little modification to the Hestenes–Stiefel method, we propose a new way to construct descent directions satisfying the sufficient descent condition. Also, an adaptive conjugacy condition and a intrinsic self-restarting mechanism are revealed, a dynamical adjustment can be regarded as the inheritance and development of properties of standard Hestenes–Stiefel method. Furthermore, we establish global convergence for general nonconvex objective function under mild condition. Numerical results show that our presented methods can be efficient for solving large-scale test problems and therefore is promising.