A modification of steepest descent method for solving large-scaled unconstrained optimization problems

 
 
 
  • Abstract
  • Keywords
  • References
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  • Abstract


    In this paper, we develop a new search direction for Steepest Descent (SD) method by replacing previous search direction from Conjugate Gradient (CG) method, , with gradient from the previous step,  for solving large-scale optimization problem. We also used one of the conjugate coefficient as a coefficient for matrix . Under some reasonable assumptions, we prove that the proposed method with exact line search satisfies descent property and possesses the globally convergent. Further, the numerical results on some unconstrained optimization problem show that the proposed algorithm is promising.

     


  • Keywords


    Steepest Descent method, Conjugate Gradient method; exact line search; global convergence.

  • References


      [1] A.-L. Cauchy, “M{é}thode g{é}n{é}rale pour la r{é}solution des syst{è}mes d’{é}quations simultan{é}es [Translated: (2010)],” Compte Rendu des S’eances L’Acad’emie des Sci., 25(2), (1847), 536–538.

      [2] M. Rivaie, M. Mamat, L. W. June, and I. Mohd, “A new class of nonlinear conjugate gradient coefficients with global convergence properties,” Appl. Math. Comput., 218(22), (2012), 11323–11332.

      [3] M. Rivaie, M. Mamat, and A. Abashar, “A new class of nonlinear conjugate gradient coefficients with exact and inexact line searches,” Appl. Math. Comput., 268, (2015), 1152–1163.

      [4] Z. Z. Abidin, M. Mamat, M. Rivaie,“A New Steepest Descent Method with Global Convergence Properties” AIP Conf. Proceedings, (2016).

      [5] H. Akaike, “On a successive transformation of probability distribution and its application to the analysis of the optimum gradient method,” Ann. Inst. Stat. Math., 11(1), (1959), 1–16.

      [6] Y. H. Xiao, M. L. Zhang, and D. Zhou, “A simple sufficient descent method for unconstrained optimization,” Math. Probl. Eng., (2010).

      [7] B. T. Polyak, “The conjugate gradient method in extremal problems,” USSR Comput. Math. Math. Phys., 9(4), (1969), 94–112.

      [8] Z. Z. Abidin, M. Mamat, M. Rivaie, and I. Mohd, “A new steepest descent method,” AIP Conference Proceedings, (2014), Vol. 1602.

      [9] M. J. D. Powell, “Restart procedures for the conjugate gradient method,” Math. Program., 12(1), 241–254, 1977.

      [10] E. D. Dolan and J. J. More, “Benchmarking Optimization Software with Performance Pro les,” 213, (2001), 201–213.


 

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Article ID: 20969
 
DOI: 10.14419/ijet.v7i3.28.20969




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