A new family of hybrid three-term conjugate gradient method for unconstrained optimization with application to image restoration and portfolio selection

Maulana Malik, Ibrahim Mohammed Sulaiman, Auwal Bala Abubakar, Gianinna Ardaneswari, Sukono

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

The conjugate gradient (CG) method is an optimization method, which, in its application, has a fast convergence. Until now, many CG methods have been developed to improve computational performance and have been applied to real-world problems. In this paper, a new hybrid three-term CG method is proposed for solving unconstrained optimization problems. The search direction is a three-term hybrid form of the Hestenes-Stiefel (HS) and the Polak-Ribiére-Polyak (PRP) CG coefficients, and it satisfies the sufficient descent condition. In addition, the global convergence properties of the proposed method will also be proved under the weak Wolfe line search. By using several test functions, numerical results show that the proposed method is most efficient compared to some of the existing methods. In addition, the proposed method is used in practical application problems for image restoration and portfolio selection.

Original languageEnglish
Pages (from-to)1-28
Number of pages28
JournalAIMS Mathematics
Volume8
Issue number1
DOIs
Publication statusPublished - 2023

Keywords

  • conjugate gradient method
  • global convergence
  • image restoration
  • portfolio selection
  • sufficient descent condition
  • unconstrained optimization

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