Enhanced Dai–Liao conjugate gradient methods for systems of monotone nonlinear equations

• M. Y. Waziri ^[2] ; K. Ahmed ^[2] ; J. Sabiu ^[3] ; A. S. Halilu ^[1]
  1. [1] Sule Lamido University

     Sule Lamido University

     Kafin Hausa, Nigeria

     
  2. [2] Bayero University
  3. [3] Yusuf Maitama Sule University

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• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 78, Nº. 1, 2021, págs. 15-51
• Idioma: inglés
• DOI: 10.1007/s40324-020-00228-9
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• Resumen

  • In this paper, we propose two conjugate gradient methods for solving large-scale monotone nonlinear equations. The methods are developed by combining the hyperplane projection method by Solodov and Svaiter (Reformulation: nonsmooth, piecewise smooth, semismooth and smoothing methods. Springer, pp 355–369, 1998) and two modified search directions of the famous Dai and Liao (Appl Math Optim 43(1): 87–101, 2001) method. It is shown that the proposed schemes satisfy the sufficient descent condition. The global convergence of the methods are established under mild conditions, and computational experiments on some benchmark test problems show that the methods are promising.