Research article

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

  • 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.

    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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  • 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.



    A Correction on

    Apomorphine-induced pathway perturbation in MPP+-treated SH-SY5Y cells by

    Jin Hwan Do AIMS Mol Sci, 2017, 4(3): 271-287. DOI: 10.3934/molsci.2017.3.271

    In the original article [1], a reference was missed. Now we add it as reference number [23]:

    Pepe D, Do JH (2016) Comparison of perturbed pathways in two different cell models for Parkinson's disease with structural equation model. J Comput Biol 23: 90-101.

    The error was introduced during production. We apologize for any inconvenience caused to the readers by this change. This error does not change the scientific conclusions of the article in any way. The original manuscript will remain online on the article webpage.




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