A Modified Davidon-Fletcher-Powell Method for Solving Nonlinear Optimization Problems

Ali Joma'a Al-Issa; Basim A. Hassan; Issam A R Moghrabi; Ibrahim M. Sulaiman

doi:10.24996/ijs.2024.65.3.25

Authors

Ali Joma'a Al-Issa Department of Mathematics, College of Computer Sciences and Mathematics University of Aleppo, Aleppo
Basim A. Hassan Department of Mathematics, College of Computers Sciences and Mathematics, University of Mosul, IRAQ
Issam A R Moghrabi 3Department of Computer Science, College of Arts and Sciences, University Central Asia, 310 Lenin Street, Naryn, 722918, Kyrgyz Republic https://orcid.org/0000-0002-4517-7630
Ibrahim M. Sulaiman Institute of Strategic Industrial Decision Modelling (ISIDM), School of Quantitative Sciences, Universiti Utara Malaysia, Sintok, 06010, Kedah, Malaysia https://orcid.org/0000-0001-5246-6636

DOI:

https://doi.org/10.24996/ijs.2024.65.3.25

Keywords:

Quasi-Newton Methods, Nonlinear optimization, Unconstrained optimization, DFP update

Abstract

One of the quasi-Newton update formulae, namely the Davidon-Fletcher-Powell method, is crucial for resolving nonlinear programming optimization problems. In order to achieve a Newton-like condition that depends on the function values and gradient vectors at each iteration, we construct an alternative positive-definite Hessian approximation in this study. The essential theorems are established to study algorithm convergence. The proposed approach is then tested on well-known test problems and then compared to the standard DFP method. The numerical outcomes demonstrate the effectiveness of the newly developed method.