A hybrid FR-DY conjugate gradient algorithm for unconstrained optimization with application in portfolio selection

Auwal Bala Abubakar; Poom Kumam; Maulana Malik; Parin Chaipunya; Abdulkarim Hassan Ibrahim; Auwal Bala Abubakar; Poom Kumam; Maulana Malik; Parin Chaipunya; Abdulkarim Hassan Ibrahim

doi:10.3934/math.2021383

AIMS Mathematics

2021, Volume 6, Issue 6: 6506-6527. doi: 10.3934/math.2021383

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Research article

A hybrid FR-DY conjugate gradient algorithm for unconstrained optimization with application in portfolio selection

1.
Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
2.
Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, Kano. Kano, Nigeria
3.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Pretoria, Medunsa-0204, South Africa
4.
Departments of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
5.
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia (UI), Depok 16424, Indonesia
6.
NCAO Research Center, Fixed Point Theory and Applications Research Group, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand

Received: 29 January 2021 Accepted: 02 April 2021 Published: 15 April 2021
MSC : 65K10, 90C26, 90C52

In this paper, we present a new hybrid conjugate gradient (CG) approach for solving unconstrained optimization problem. The search direction is a hybrid form of the Fletcher-Reeves (FR) and the Dai-Yuan (DY) CG parameters and is close to the direction of the memoryless Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton approach. Independent of the line search, the search direction of the new approach satisfies the descent condition and possess the trust region. We establish the global convergence of the approach for general functions under the Wolfe-type and Armijo-type line search. Using the CUTEr library, numerical results show that the propose approach is more efficient than some existing approaches. Furthermore, we give a practical application of the new approach in optimizing risk in portfolio selection.
- unconstrained optimization,
- hybrid three-term conjugate gradient method,
- global convergence,
- portfolio selection
Citation: Auwal Bala Abubakar, Poom Kumam, Maulana Malik, Parin Chaipunya, Abdulkarim Hassan Ibrahim. A hybrid FR-DY conjugate gradient algorithm for unconstrained optimization with application in portfolio selection[J]. AIMS Mathematics, 2021, 6(6): 6506-6527. doi: 10.3934/math.2021383

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Abstract

In this paper, we present a new hybrid conjugate gradient (CG) approach for solving unconstrained optimization problem. The search direction is a hybrid form of the Fletcher-Reeves (FR) and the Dai-Yuan (DY) CG parameters and is close to the direction of the memoryless Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton approach. Independent of the line search, the search direction of the new approach satisfies the descent condition and possess the trust region. We establish the global convergence of the approach for general functions under the Wolfe-type and Armijo-type line search. Using the CUTEr library, numerical results show that the propose approach is more efficient than some existing approaches. Furthermore, we give a practical application of the new approach in optimizing risk in portfolio selection.

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