IJPAM: Volume 119, No. 1 (2018)




Issam A.R. Moghrabi
Department of M.I.S.
College of Business Administration
Gulf University for Science and Technology (GUST)
P.O. Box 7207, Hawally 32093, KUWAIT


This paper presents a framework model for building minimum curvature Multi-step methods. The Multi-step methods were derived in [6,7] and have consistently outperformed the traditional quasi-Newton methods that satisy the classical linear Secant equation. The methods derived here aim at improving further the Multi-step methods by ensuring that the interpolating curve used in updating the Hessian approximation has minimum a curvature. The model used in the derivation of such methods utilizes a free parameter that is employed as a tuning variable. The idea of minimizing the curvature of the interpolant was introduced in [2]. The encouraging results justify the investigation of these methods further. The algorithms derived are benchmarked against some of the most successful quasi-Newton methods such as the standard BFGS and the methods derived in [2,5,6,7]. The results of the numerical experiments indicate that the improvements obtained are substantially good and that the methods are indeed promising.


Received: April 25, 2018
Revised: June 11, 2018
Published: June 13, 2018

AMS Classification, Key Words

AMS Subject Classification: 65K10
Key Words and Phrases: unconstrained optimization, conjugate gradient methods,variable metric methods

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How to Cite?

DOI: 10.12732/ijpam.v119i1.11 How to cite this paper?

International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 119
Issue: 1
Pages: 131 - 143

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