New Spectral Idea for Conjugate Gradient Methods and its Global Convergence Theorems

Authors

  • Aseel Qasim Department of Mathematics, College of Education of Pure Sciences, University of Mosul
  • Zinah Salih Department Mathematics, College of Computers Sciences and Mathematics, University of Mosul

DOI:

https://doi.org/10.29020/nybg.ejpam.v15i2.4364

Keywords:

Conjugate gradient, spectral, unconstrained optimization, Global convergence, descent property

Keywords:

Conjugate gradient, spectral, unconstrained optimization, Global convergence, descent property

Abstract

Recently, the unconstrained optimization conjugate gradient methods have been widely utilized, especially for problems that are known as large-scale problems. This work proposes a new spectral gradient coefficient obtained from a convex linear combination of two different gradient coefficients to solve unconstrained optimization problems. One of the most essential features of
our suggested strategy is to guarantee the suitable subsidence direction of the line search precision. Furthermore, the proposed strategy is more effective than previous conjugate gradient approaches and stationery, which have been observed in the test problem. However, when it is compared to other conjugate gradient methods, such as FR methods, the proposed method confirmed the globally convergent, indicating that it can be used in scientific data computation.

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How to Cite

Qasim, A. ., & Salih, Z. (2022). New Spectral Idea for Conjugate Gradient Methods and its Global Convergence Theorems. European Journal of Pure and Applied Mathematics, 15(2), 784–795. https://doi.org/10.29020/nybg.ejpam.v15i2.4364