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Issam A. R. Moghrabi



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Issam A. R. Moghrabi


WSEAS Transactions on Mathematics


Print ISSN: 1109-2769
E-ISSN: 2224-2880

Volume 18, 2019

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.


Volume 18, 2019



A New Formulation for Quasi-Newton Methods

AUTHORS: Issam A. R. Moghrabi

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We develop a framework for the construction of multi-step quasi-Newton methods which utilize values of the objective function. The model developed here is constructed via interpolants of the m+1 most recent iterates / gradient evaluations, and possesses double free parameters which introduce an additional degree of flexibility. This permits the interpolating polynomials to exploit function-values which are readily available at each iteration. A new algorithm is derived for which function values are incorporated in the update of the inverse Hessian approximation at each iteration, in an attempt to accelerate convergence. The idea of incorporating function values is not new within the context of quasi-Newton methods but the presentation made in this paper presents a new approach for such algorithms. It has been shown in several earlier works that Including function values data in the update of the Hessian approximation numerically improves the convergence of Secant-like methods. The numerical performance of the new method is assessed with promising results.

KEYWORDS: Unconstrained optimization, quasi-Newton methods, multi-step methods, function value algorithms, nonlinear programming, Newton method

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WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 18, 2019, Art. #10, pp. 79-84


Copyright Β© 2018 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

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