An Efficient Limited Memory Multi-Step Quasi-Newton Method

Issam A. R. Moghrabi () and Basim A. Hassan
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Issam A. R. Moghrabi: Department of Information Systems and Technology, Kuwait Technical College, Abu-Halifa 54753, Kuwait
Basim A. Hassan: Department of Mathematics, College of Computer Sciences and Mathematics, University of Mosul, Mosul 41002, Iraq

Mathematics, 2024, vol. 12, issue 5, 1-13

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.

Keywords: quasi-Newton methods; multi-step methods; unconstrained optimization; limited memory methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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