Globally convergent conjugate gradient algorithms for large-scale unconstrained optimization

Authors

  • Mehamdia Abd Elhamid Department of Mathematics, Universite M’Hamed Bougara of Boumerdes, Algeria
  • Ali Joma Alissa Education Depertment, Liwa University, Abu Dhabi, United Arab Emirates
  • Basim A. Hassan College of Computers Sciences and Mathematics, university of Mosul, Iraq
  • Bouaziz Tayeb Department of Mathematics, Universite M’Hamed Bougara of Boumerdes, Algeria
  • Ismat Suleiman Salem Abu Sahyoun Liwa University, Saeed Bin Ahmed Al Otaiba Street (Al Najda Street previously), Al Danah, Baniyas Tower B, Abu Dhabi, United Arab Emirates

DOI:

https://doi.org/10.19139/soic-2310-5070-3418

Keywords:

Hybrid conjugate gradient method, Inexact line search, Descent condition, Global convergence, Numerical comparisons.

Abstract

Optimization techniques are extensively employed to obtain numerical solutions to optimal control problems that appear in scientific and engineering computations, particularly in the context of large-scale problems. In this paper, drawing on some modern and computationally efficient approaches, we introduce two modified conjugate gradient methods (referred to as the IHS and IPRP methods) for unconstrained optimization. Under the strong Wolfe line search (SWLS), the proposed methods are shown to generate sufficient descent at every iteration. Furthermore, we establish that these methods are globally convergent for arbitrary objective functions, provided that the line search satisfies the strong Wolfe conditions. Numerical experiments, interpreted using the Dolan and Mor\'{e} performance profiles, confirm the efficiency of the IHS and IPRP methods in comparison with several existing algorithms.

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Published

2026-07-01

How to Cite

Abd Elhamid, M., Alissa, A. J., Hassan, B. A., Tayeb, B., & Abu Sahyoun, I. S. S. (2026). Globally convergent conjugate gradient algorithms for large-scale unconstrained optimization. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-3418

Issue

Online First

Section

Research Articles

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Copyright (c) 2026 Mehamdia Abd Elhamid, Ali Joma Alissa, Basim A. Hassan, Bouaziz Tayeb, Ismat Suleiman Salem Abu Sahyoun

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