Published June 1, 2021 | Version v1
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Two-versions of descent conjugate gradient methods for large-scale unconstrained optimization

  • 1. Department of Mathematics, College of Sciences, University of Kirkuk, Iraq
  • 2. Department of Mathematics, College of Computers Sciences and Mathematics, University of Mosul, Iraq

Description

The conjugate gradient methods are noted to be exceedingly valuable for solving large-scale unconstrained optimization problems since it needn't the storage of matrices. Mostly the parameter conjugate is the focus for conjugate gradient methods. The current paper proposes new methods of parameter of conjugate gradient type to solve problems of large-scale unconstrained optimization. A Hessian approximation in a diagonal matrix form on the basis of second and third-order Taylor series expansion was employed in this study. The sufficient descent property for the proposed algorithm are proved. The new method was converged globally. This new algorithm is found to be competitive to the algorithm of fletcher-reeves (FR) in a number of numerical experiments.

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