@article{f0e8ded39e8e4314ba8b86683e6c913c,
title = "A hybrid fr-dy conjugate gradient algorithm for unconstrained optimization with application in portfolio selection",
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.",
keywords = "Global convergence, Hybrid three-term conjugate gradient method, Portfolio selection, Unconstrained optimization",
author = "Abubakar, {Auwal Bala} and Poom Kumam and Maulana Malik and Parin Chaipunya and Ibrahim, {Abdulkarim Hassan}",
note = "Funding Information: The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Also, the (first) author, (Dr. Auwal Bala Abubakar) would like to thank the Postdoctoral Fellowship from King Mongkut{\textquoteright}s University of Technology Thonburi (KMUTT), Thailand. Moreover, this research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2021 under project number 64A306000005. The first author acknowledge with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University. Funding Information: The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Also, the (first) author, (Dr. Auwal Bala Abubakar) would like to thank the Postdoctoral Fellowship from King Mongkut?s University of Technology Thonburi (KMUTT), Thailand. Moreover, this research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2021 under project number 64A306000005. The first author acknowledge with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University. Publisher Copyright: {\textcopyright} 2021 the Author(s), licensee AIMS Press.",
year = "2021",
doi = "10.3934/math.2021383",
language = "English",
volume = "6",
pages = "6506--6527",
journal = "AIMS Mathematics",
issn = "2473-6988",
publisher = "AIMS Press",
number = "6",
}