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Research Article | Open Access

An optimal choice Dai-Liao conjugate gradient algorithm for unconstrained optimization and portfolio selection

Jamilu Sabi'u1, Ibrahim Mohammed Sulaiman2,3( ), P. Kaelo4, Maulana Malik5, Saadi Ahmad Kamaruddin2( )
Department of Mathematics, Yusuf Maitama Sule University Kano, Nigeria
Institute of Strategic Industrial Decision Modelling, School of Quantitative Sciences, Universiti Utara Malaysia, Sintok 06010, Malaysia
Faculty of Education and Arts, Sohar University, Sohar 311, Oman
Department of Mathematics, University of Botswana, Private Bag UB00704, Gaborone, Botswana
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok 16424, Indonesia
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Abstract

In this research, we propose an optimal choice for the non-negative constant in the Dai-Liao conjugate gradient formula based on the prominent Barzilai-Borwein approach by leveraging the nice features of the Frobenius matrix norm. The global convergence of the new modification is demonstrated using some basic assumptions. Numerical comparisons with similar algorithms show that the new approach is reliable in terms of the number of iterations, computing time, and function evaluations for unconstrained minimization, portfolio selection and image restoration problems.

Keywords

unconstrained optimizationBB approachdescent propertyglobal convergence
CLC number: 90C26, 90C30

References

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AIMS Mathematics
Volume 9 Issue 1,
January 2024
Pages 642-664
DOI: 10.3934/math.2024034

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Cite this article:
Sabi'u J, Sulaiman IM, Kaelo P, et al. An optimal choice Dai-Liao conjugate gradient algorithm for unconstrained optimization and portfolio selection. AIMS Mathematics, 2024, 9(1): 642-664. https://doi.org/10.3934/math.2024034

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Received: 18 August 2023
Revised: 16 October 2023
Accepted: 18 October 2023
Published: 15 January 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)