An Investigation Of A New Hybrid Conjugates Gradient Approach For Unconstrained Optimization Problems

Rahma F. Aziz; Maha S. Younis; Marwan S. Jameel

doi:10.62383/bilangan.v2i4.136

Authors

Rahma F. Aziz Mosul University
Maha S. Younis Mosul University
Marwan S. Jameel Mosul University

DOI:

https://doi.org/10.62383/bilangan.v2i4.136

Keywords:

Numerical optimization, Unconstrained objective function, Hybrid gradient methods, Global convergence, Numerical experiment

Abstract

This work introduces a novel hybrid conjugate gradient (CG) technique for tackling unconstrained optimisation problems with improved efficiency and effectiveness. The parameter is computed as a convex combination of the standard conjugate gradient techniques using and . Our proposed method has shown that when using the strong Wolfe-line-search(SWC) under specific conditions, it achieves global theoretical convergence. In addition, the new hybrid CG approach has the ability to generate a search direction that moves downward with each iteration. The quantitative findings obtained by applying the recommended technique about 30 functions with varying dimensions clearly illustrate its effectiveness and potential.

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