Title: A new secant-like quasi-Newton method for unconstrained optimisation

Authors: Issam A.R. Moghrabi

Addresses: Accounting and MIS Department, College of Business, Gulf University for Science and Technology, Kuwait

Abstract: The secant equation traditionally constitutes the basis of quasi-Newton methods, as the updated Hessian approximations satisfy the equation on each iteration. Modified versions of the secant relation have recently been the focus of several papers with encouraging outcomes. This paper continues with that idea where a secant-like modification that utilises nonlinear quantities in constructing the Hessian (or its inverse) approximation updates is derived. The technique takes advantage of data readily computed from the two most recent steps. Thus, it offers a substitute to the secant equation to produce better Hessian approximations that result in accelerated convergence to the objective function minimiser. The reported results provide adequate evidence to suggest that the proposed method is promising and deserves attention.

Keywords: quasi-Newton methods; secant-like methods; BFGS; unconstrained optimisation; multi-step methods.

DOI: 10.1504/IJOR.2024.136006

International Journal of Operational Research, 2024 Vol.49 No.1, pp.65 - 84

Received: 07 Sep 2020
Accepted: 28 Mar 2021
Published online: 12 Jan 2024 *

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