Have a personal or library account? Click to login
Application of a globally convergent hybrid conjugate gradient method in portfolio optimization Cover

Application of a globally convergent hybrid conjugate gradient method in portfolio optimization

By: P. Mtagulwa,  P. Kaelo,  T. Diphofu and  K. Kaisara  
Open Access
|Jun 2024

References

  1. A. B. Abubakar, P. Kumam, M. Malik, P. Chaipunya and A. H. Ibrahim, A hybrid FR-DY conjugate gradient algorithm for unconstrained optimization with application in portfolio selection. AIMS Math, 6(6) (2021), 6506-6527.
  2. O. J. Adeleke, M. O. Olusanya and I. A. Osinuga, A PRP-HS Type Hybrid Nonlinear Conjugate Gradient Method for Solving Unconstrained Optimization Problems, In: Silhavy, R., Silhavy, P., Prokopova, Z (eds) Intelligent Systems Applications in Software Engineering. CoMeSySo 2019 (2019). Advances in Intelligent Systems and Computing, 1046, Springer, Cham.
  3. A. Alhawarat, M. Mamat, M. Rivaie and Z. Salleh, An efficient hybrid conjugate gradient method with the strong Wolfe-Powell line search, Math. Probl. Eng., 2015: 103517 (2015).
  4. N. Andrei, An unconstrained optimization test functions collection, Adv. Model. Optim., 10(1) (2008), 147–161.
  5. A. M. Awwal, I. M. Sulaiman, M. Malik, M. Mamat, P. Kumam and K. Sitthithakerngkiet, A spectral RMIL+ conjugate gradient method for unconstrained optimization with applications in portfolio selection and motion control. IEEE Access, 9 (2021), 75398-75414.
  6. M. C. Bartholomew-Biggs, Nonlinear Optimization with Financial Applications. Kluwer Academic Publishers, Boston (2006).
  7. M. C. Bartholomew-Biggs and S. J. Kane, A global optimization problem in portfolio selection. Comput. Manag. Sci., 6 (2009) 329-345.
  8. Y. H. Dai, A family of hybrid conjugate gradient methods for unconstrained optimization, Math. Comput., 72(243) (2003), 1317-1328.
  9. Y. H. Dai and L. Liao, New conjugacy conditions and related nonlinear conjugate gradient methods, Appl. Math. Optim., 43 (2001), 87-101.
  10. Z. Dai and F. Wen, Another improved Wei-Yao-Liu nonlinear conjugate gradient method with sufficient descent property, Appl. Math. Comput., 218(14) (2012), 7421-7430.
  11. T. Diphofu and P. Kaelo, Another three-term conjugate gradient method close to the memoryless BFGS for large scale unconstrained optimization problems, Mediterr. J Math., 18:211 (2021).
  12. T. Diphofu, P. Kaelo and A. R. Tufa, A modified nonlinear conjugate gradient algorithm for unconstrained optimization and portfolio selection problems. RAIRO Oper. Res., 57(2) (2023), 817-835.
  13. E. D. Dolan, J. J. Moré, Benchmarking optimization software with performance profiles, Math. Program., 91 (2002), 201-214.
  14. M. Fang, M. Wang, M. Sun and R. Chen, A Modified Hybrid Conjugate Gradient Method for Unconstrained Optimization, J. Math., 2021(1) (2021), 1-9.
  15. R. Fletcher, Practical methods of optimization, Unconstrained Optimization, John Wiley & Sons, New York 1(1987).
  16. R. Fletcher and C. M. Reeves, Function minimization by conjugate gradients, Computer J., 7(2) (1964), 149-154.
  17. H. Guan and S. Wang, A Modified Conjugate Gradient Method for Solving Large-Scale Nonlinear Equations, Math. Probl. Eng., 2021:9919595 (2021), https://doi.org/10.1155/2021/9919595.
  18. W. W. Hager and H. Zhang, A survey of nonlinear conjugate gradient methods, Pacific J. Optim., 2 (2011), 35-58.
  19. M. R. Hestenes and E. Stiefel, Methods of conjugate gradients for solving linear systems, J Res. Nat. Bureau Stand., 49(6) (1952), 409-436.
  20. X. Jiang, J. Jian, D. Song and P. Liu, An improved Polak-Ribiére-Polyak conjugate gradient method with an efficient restart direction, Comput. Appl. Math., 40(174) (2021), 1-24.
  21. X. Jiang, W. Liao, J. Yin, J. Yin and J. Jian, A new family of hybrid three-term conjugate gradient methods with applications in image restoration, Numer. Algor., 91(2) (2022), 1-31.
  22. Y. Liu and C. Storey, Efficient generalized conjugate gradient algorithms, Part 1: Theory, J Optim. Theory Appl., 69(1) (1991), 129-137.
  23. H. Markowitz, Portfolio Selection, J. Finance, 7(1) (1952), 77-91.
  24. P. Mtagulwa and P. Kaelo, An efficient modified PRP-FR hybrid conjugate gradient method for solving unconstrained optimization problems, Appl. Numer. Math., 145 (2019), 111–120.
  25. A. A. Mustafa, New Spectral LS conjugate gradient method for nonlinear unconstrained optimization, Int. J Comput. Math.,100 (2023), 838–846.
  26. E. Polak and G. Ribiére, Note sur la convergence de directions conjugées, Rev. Francaise Informat Recherche Opèrationelle, 3e Année, 16 (1969), 35–43.
  27. B. T. Polyak, The conjugate gradient method in extreme problems, USSR Comput. Math. Math. Phys, 9(4) (1969), 94-112.
  28. I. M. Sulaiman, M. Malik, A. M. Awwal, P. Kumam, M. Mamat and S. Al-Ahmad, On three-term conjugate gradient method for optimization problems with applications on COVID-19 model and robotic motion control, Adv Cont Discr Mod., 2022:1 (2022). https://doi.org/10.1186/s13662-021-03638-9.
  29. Z. Wei, S. Yao and L. Liu, The convergence properties of some new conjugate gradient methods, Appl. Math. Comput., 183(2) (2006), 1341-1350.
  30. L. Zhang, An improved Wei-Yao-Liu nonlinear conjugate gradient method for optimization computation, Appl. Math. Comput., 215(6) (2009), 2269-2274.
  31. G. Zoutendijk, Nonlinear programming, computational methods, In: J. Abadie Ed., Integer and Nonlinear Programming, North-Holland, Amsterdam, 1970, pp. 37-86.
DOI: https://doi.org/10.2478/jamsi-2024-0003 | Journal eISSN: 1339-0015 | Journal ISSN: 1336-9180
Language: English
Page range: 33 - 52
Published on: Jun 3, 2024
Published by: University of Ss. Cyril and Methodius in Trnava
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2024 P. Mtagulwa, P. Kaelo, T. Diphofu, K. Kaisara, published by University of Ss. Cyril and Methodius in Trnava
This work is licensed under the Creative Commons Attribution 4.0 License.