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An Efficient Limited Memory Multi-Step Quasi-Newton Method

Author

Listed:
  • Issam A. R. Moghrabi

    (Department of Information Systems and Technology, Kuwait Technical College, Abu-Halifa 54753, Kuwait
    Department of Computer Science, School of Arts and Science, University of Central Asia, Naryn 722918, Kyrgyzstan)

  • Basim A. Hassan

    (Department of Mathematics, College of Computer Sciences and Mathematics, University of Mosul, Mosul 41002, Iraq)

Abstract

This paper is dedicated to the development of a novel class of quasi-Newton techniques tailored to address computational challenges posed by memory constraints. Such methodologies are commonly referred to as “limited” memory methods. The method proposed herein showcases adaptability by introducing a customizable memory parameter governing the retention of historical data in constructing the Hessian estimate matrix at each iterative stage. The search directions generated through this novel approach are derived from a modified version closely resembling the full memory multi-step BFGS update, incorporating limited memory computation for a singular term to approximate matrix–vector multiplication. Results from numerical experiments, exploring various parameter configurations, substantiate the enhanced efficiency of the proposed algorithm within the realm of limited memory quasi-Newton methodologies category.

Suggested Citation

  • Issam A. R. Moghrabi & Basim A. Hassan, 2024. "An Efficient Limited Memory Multi-Step Quasi-Newton Method," Mathematics, MDPI, vol. 12(5), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:768-:d:1351155
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    References listed on IDEAS

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    1. Matteo Lapucci & Pierluigi Mansueto, 2023. "A limited memory Quasi-Newton approach for multi-objective optimization," Computational Optimization and Applications, Springer, vol. 85(1), pages 33-73, May.
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