A hybrid IFR-IDY conjugate gradient algorithm for unconstrained optimization and its application in portfolio selection

Authors

  • Diva Marchandra Mulansari
    Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok 16424, Indonesia
  • Maulana Malik
    Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok 16424, Indonesia
  • Sindy Devila
    Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok 16424, Indonesia
  • Ibrahim Mohammed Sulaiman
    College of Applied and Health Sciences, A’Sharqiyah University, Ibra 400, Sultanate of Oman
  • Dian Lestari
    Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok 16424, Indonesia
  • Fevi Novkaniza
    Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok 16424, Indonesia
  • Fida Fathiyah Addini
    Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok 16424, Indonesia

Keywords:

Inexact line search, Global convergence, Investment, Numerical optimization, Strong Wolfe

Abstract

This study introduces the Improved Fletcher-Reeves (IFR)-Improved Dai-Yuan (IDY) hybrid conjugate gradient method, which combines the strengths of the IFR and IDY parameters through a minimum-operator strategy to enhance robustness in unconstrained optimization. The method is shown to satisfy descent and global convergence properties under the strong Wolfe line search. Numerical experiments on 134 benchmark functions demonstrate that IFR-IDY achieves superior performance, solving 98 problems more than IFR and IDY and exhibiting faster CPU times and fewer iterations in most cases. The method is also used to solve an IDX30 portfolio optimization problem, which results in an optimal allocation with an expected return of 0.00042 and a risk of 0.000050545. These results highlight the efficiency of IFR-IDY and its practical applicability in real-world decision-making.

Dimensions

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Performance profile curves based on number of iteration.

Published

2026-02-16

How to Cite

A hybrid IFR-IDY conjugate gradient algorithm for unconstrained optimization and its application in portfolio selection. (2026). Journal of the Nigerian Society of Physical Sciences, 8(1), 3105. https://doi.org/10.46481/jnsps.2026.3105

Issue

Volume 8, Issue 1, February 2026

Section

Mathematics & Statistics
Copyright & Licensing

Copyright (c) 2025 Diva Marchandra Mulansari, Maulana Malik, Sindy Devila, Ibrahim Mohammed Sulaiman, Dian Lestari, Fevi Novkaniza, Fida Fathiyah Addini (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

A hybrid IFR-IDY conjugate gradient algorithm for unconstrained optimization and its application in portfolio selection. (2026). Journal of the Nigerian Society of Physical Sciences, 8(1), 3105. https://doi.org/10.46481/jnsps.2026.3105

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