Skip to main content
Log in

A Structured Fletcher-Revees Spectral Conjugate Gradient Method for Unconstrained Optimization with Application in Robotic Model

  • Research
  • Published:
Operations Research Forum Aims and scope Submit manuscript

Abstract

In order to address the numerical performance issue associated with Fletcher and Reeves conjugate gradient method, a variation of spectral conjugate gradient method is presented in this paper. The spectral parameter is obtained in such a way that any line search rule is not necessary for the search direction to be sufficiently descent. The proposed scheme is globally convergent under some suitable conditions. When compared to several conventional conjugate gradient methods including CG_Descent, the preliminary numerical experiments on some set of test functions demonstrate the usefulness of the suggested method. Additionally, the effectiveness of the method is further illustrated by its success in solving robotic problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Algorithm 1
Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Data Availability

All the relevant data for this study are available within the paper.

Code Availability

The codes of the current study are available upon request from the corresponding author.

References

  1. Salihu N, Odekunle M, Waziri M, Halilu A (2020) A new hybrid conjugate gradient method based on secant equation for solving large scale unconstrained optimization problems. Iran J Optim 12(1):33–44

    Google Scholar 

  2. Fletcher R, Reeves CM (1964) Function minimization by conjugate gradients. Comput J 7(2):149–154

    Article  MathSciNet  Google Scholar 

  3. Nasiru S, Mathew RO, Mohammed YW, Abubakar SH, Suraj S (2021) A Dai-Liao hybrid conjugate gradient method for unconstrained optimization. Int J Ind Optim 2(2):69–84

    Article  Google Scholar 

  4. Zoutendijk G (1970) Nonlinear programming, computational methods. In: Abadie J (ed) Integer and Nonlinear Programming. North-Holland, Amsterdam, pp 37–86

    Google Scholar 

  5. Al-Baali M (1985) Descent property and global convergence of the Fletcher-Reeves method with inexact line search. IMA J Numer Anal 5(1):121–124

    Article  MathSciNet  Google Scholar 

  6. Salihu N, Odekunle MR, Saleh AM, Salihu S (2021) A Dai-Liao hybrid Hestenes-Stiefel and Fletcher-Fevees methods for unconstrained optimization. Int J Ind Optim 2(1):33–50

    Article  Google Scholar 

  7. Andrei N (2020) Nonlinear conjugate gradient methods for unconstrained optimization. Springer Cham

  8. Raydan M (1997) The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem. SIAM J Optim 7(1):26–33

    Article  MathSciNet  Google Scholar 

  9. Birgin EG, Martínez JM, Raydan M (2000) Nonmonotone spectral projected gradient methods on convex sets. SIAM J Optim 10(4):1196–1211

    Article  MathSciNet  Google Scholar 

  10. Birgin EG, Martínez JM (2001) A spectral conjugate gradient method for unconstrained optimization. Appl Math Optim 43(2):117–128

    Article  MathSciNet  Google Scholar 

  11. Zhang L, Zhou W, Li D (2006) Global convergence of a modified Fletcher-Reeves conjugate gradient method with Armijo-type line search. Numer Math 104(4):561–572

    Article  MathSciNet  Google Scholar 

  12. Liu J, Feng Y, Zou L (2019) A spectral conjugate gradient method for solving large-scale unconstrained optimization. Comput Math Appl 77(3):731–739

    Article  MathSciNet  Google Scholar 

  13. Awwal AM, Sulaiman IM, Maulana M, Mustafa M, Poom K, Kanokwan S (2021) A spectral RMIL+ conjugate gradient method for unconstrained optimization with applications in portfolio selection and motion control. IEEE Access 9:75398–75414

    Article  Google Scholar 

  14. Barz T, Körkel S, Wozny G et al (2015) Nonlinear ill-posed problem analysis in model-based parameter estimation and experimental design. Comput Chem Eng 77:24–42

    Article  Google Scholar 

  15. Jian J, Yang L, Jiang X, Liu P, Liu M (2020) A spectral conjugate gradient method with descent property. Mathematics 8(2):280

    Article  Google Scholar 

  16. Salihu N, Kumam P, Awwal AM, Sulaiman IM, Seangwattana T (2023) The global convergence of spectral RMIL conjugate gradient method for unconstrained optimization with applications to robotic model and image recovery. PLoS ONE 18(3):e0281250

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  17. Zhongbo S, Xue C, Yingying G, Yuncheng G, Yue S (2017) Two modified PRP conjugate gradient methods and their global convergence for unconstrained optimization. 2017 29th Chinese Control And Decision Conference (CCDC). pp 786–790

  18. Polak E, Ribiere G (1969) Note sur la convergence de methodes de directions conjuguees. USSR Comput Math Math Phys 9(4):94–112

    Google Scholar 

  19. Polyak BT (1967) A general method for solving extremal problems. Dokl Akad Nauk SSSR 174(1):33–36

    MathSciNet  Google Scholar 

  20. Wu X (2015) A new spectral Polak-ribière-Polak conjugate gradient method. ScienceAsia 41:345–349

    Article  Google Scholar 

  21. Hager W, Zhang H (2006) Algorithm 851: CG DESCENT, a conjugate gradient method with guaranteed descent. ACM Trans Math Softw 32(1):113–137

    Article  MathSciNet  Google Scholar 

  22. Momin J, Xin-She Y (2013) A literature survey of benchmark functions for global optimization problems. Int J Math Model Numer Optim 4(2):150–194

  23. Dolan ED, Moré JJ (2002) Benchmarking optimization software with performance profiles. Math Program 91(2):201–213

    Article  MathSciNet  Google Scholar 

  24. Renfrew A (2004) Introduction to robotics: mechanics and control. Int J Electr Eng Educ 41(4):388

    Article  Google Scholar 

  25. Zhang Y, He L, Hu C, Guo J, Li J, Shi Y (2019) General four-step discrete-time zeroing and derivative dynamics applied to time-varying nonlinear optimization. J Comput Appl Math 347:314–329

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors acknowledged the support of the National Research Council of Thailand (NRCT) under Research Grants for Talented Mid-Career Researchers (Contract no. N41A640089) and Research and National Science Innovation Fund (NSRF), King Mongkut’s University of Technology North Bangkok with Contract No. KMUTNB-FF-66-36. In addition, the first author also acknowledged the support of the Petchra Pra Jom Klao Doctoral Research Scholarship from King Mongkut’s University of Technology Thonburi with Contract No. 52/2564 and the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT.

Funding

The work of these authors is supported by the National Science Research and Innovation Fund (NSRF), King Mongkut’s University of Technology North Bangkok with Contract No. KMUTNB-FF-66-36.

Author information

Authors and Affiliations

Authors

Contributions

Nasiru Salihu and Aliyu Muhammed Auwal: Conceptualization, Methodology, Coding. Nasiru Salihu: Writing-Original draft. Nasiru Salihu, Ibrahim Arzuka and Thidaporn Seangwattana: Visualization, Investigation, Validation. Poom Kumam: Supervision. Poom Kumam and Thidaporn Seangwattana. Validating the Experiment. Nasiru Salihu, Poom Kumam, Aliyu Muhammed Auwal and Thidaporn Seangwattana: Writing- Reviewing and Editing the manuscript.

Corresponding author

Correspondence to Poom Kumam.

Ethics declarations

Ethical Approval

Not applicable.

Consent to Participate

Not applicable.

Consent for Publication

Not applicable.

Competing Interests

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article is part of the Topical Collection on Optimization, Control, and Machine Learning for Interdependent Networks

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Salihu, N., Kumam, P., Awwal, A.M. et al. A Structured Fletcher-Revees Spectral Conjugate Gradient Method for Unconstrained Optimization with Application in Robotic Model. Oper. Res. Forum 4, 81 (2023). https://doi.org/10.1007/s43069-023-00265-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s43069-023-00265-w

Keywords

Mathematics Subject Classification

Navigation