Title: A new approach for non-convex optimisation problems applied to Hump and benchmark functions

Authors: Fadila Leslous; Mouloud Goubi; Mohand Ouanes

Addresses: Laboratory of Operational Research and Mathematics (LAROMAD), Department of Mathematics, Faculty of Sciences, University Mouloud Mammeri of Tizi-Ouzou Algeria, Tizi Ouzou, Algeria ' Department of Mathematics, Faculty of Sciences, University Mouloud Mammeri of Tizi-Ouzou Algeria, Tizi Ouzou, Algeria; Laboratory of Algebra and Number Theory (LATN), USTHB Algeirs, Bab Ezzouar, Algeria ' Laboratory of Operational Research and Mathematics (LAROMAD), Department of Mathematics, Faculty of Sciences, University Mouloud Mammeri of Tizi-Ouzou Algeria, Tizi Ouzou, Algeria

Abstract: A new approach for solving multivariate global optimisation problems with a single objective function or multiobjective functions. Our method consists in reducing the multivariate case to the univariate case and then we solve an univariate global optimisation problem over an interval of ℝ. To do this, a change of variables combined with algebraic tools and Newton method are used. An algorithm is derived to find a global optimal solution of the original problem.

Keywords: multi-objective optimisation; global optimisation; Hump functions; non-convex optimisation; Newton algorithm.

DOI: 10.1504/IJMOR.2023.132481

International Journal of Mathematics in Operational Research, 2023 Vol.25 No.3, pp.323 - 342

Received: 16 Nov 2021
Accepted: 21 May 2022
Published online: 24 Jul 2023 *

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