IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i23p4411-d981214.html
   My bibliography  Save this article

Comparative Analysis of Accelerated Models for Solving Unconstrained Optimization Problems with Application of Khan’s Hybrid Rule

Author

Listed:
  • Vladimir Rakočević

    (Serbian Academy of Sciences and Arts, Kneza Mihajla 35, 11000 Belgrade, Serbia
    Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18106 Niš, Serbia)

  • Milena J. Petrović

    (Faculty of Sciences and Mathematics, University of Pristina in Kosovska Mitrovica, Lole Ribara 29, 38220 Kosovska Mitrovica, Serbia)

Abstract

In this paper, we follow a chronological development of gradient descent methods and its accelerated variants later on. We specifically emphasise some contemporary approaches within this research field. Accordingly, a constructive overview over the class of hybrid accelerated models derived from the three-term hybridization process proposed by Khan is presented. Extensive numerical test results illustrate the performance profiles of hybrid and non-hybrid versions of chosen accelerated gradient models regarding the number of iterations, CPU time, and number of function evaluation metrics. Favorable outcomes justify this hybrid approach as an accepted method in developing new efficient optimization schemes.

Suggested Citation

  • Vladimir Rakočević & Milena J. Petrović, 2022. "Comparative Analysis of Accelerated Models for Solving Unconstrained Optimization Problems with Application of Khan’s Hybrid Rule," Mathematics, MDPI, vol. 10(23), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4411-:d:981214
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/23/4411/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/23/4411/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Predrag S. Stanimirović & Gradimir V. Milovanović & Milena J. Petrović & Nataša Z. Kontrec, 2015. "A Transformation of Accelerated Double Step Size Method for Unconstrained Optimization," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-8, April.
    2. David G. Luenberger & Yinyu Ye, 2008. "Linear and Nonlinear Programming," International Series in Operations Research and Management Science, Springer, edition 0, number 978-0-387-74503-9, March.
    3. Milena J. Petrović & Predrag S. Stanimirović, 2014. "Accelerated Double Direction Method for Solving Unconstrained Optimization Problems," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-8, April.
    4. Milena J. Petrović & Predrag S. Stanimirović & Nataša Kontrec & Julija Mladenović, 2018. "Hybrid Modification of Accelerated Double Direction Method," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-8, November.
    5. Wenyu Sun & Ya-Xiang Yuan, 2006. "Optimization Theory and Methods," Springer Optimization and Its Applications, Springer, number 978-0-387-24976-6, June.
    6. Neculai Andrei, 2020. "Nonlinear Conjugate Gradient Methods for Unconstrained Optimization," Springer Optimization and Its Applications, Springer, number 978-3-030-42950-8, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tiantian Zhao & Wei Hong Yang, 2023. "A Nonlinear Conjugate Gradient Method Using Inexact First-Order Information," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 502-530, August.
    2. Milena J. Petrović & Dragana Valjarević & Dejan Ilić & Aleksandar Valjarević & Julija Mladenović, 2022. "An Improved Modification of Accelerated Double Direction and Double Step-Size Optimization Schemes," Mathematics, MDPI, vol. 10(2), pages 1-18, January.
    3. Halilu, Abubakar Sani & Majumder, Arunava & Waziri, Mohammed Yusuf & Ahmed, Kabiru, 2021. "Signal recovery with convex constrained nonlinear monotone equations through conjugate gradient hybrid approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 520-539.
    4. Shahmohammadi, Ali & Sioshansi, Ramteen & Conejo, Antonio J. & Afsharnia, Saeed, 2018. "Market equilibria and interactions between strategic generation, wind, and storage," Applied Energy, Elsevier, vol. 220(C), pages 876-892.
    5. Alp Atakan & Mehmet Ekmekci & Ludovic Renou, 2021. "Cross-verification and Persuasive Cheap Talk," Papers 2102.13562, arXiv.org, revised Apr 2021.
    6. Arthur Medeiros & Thales Ramos & José Tavares de Oliveira & Manoel F. Medeiros Júnior, 2020. "Direct Voltage Control of a Doubly Fed Induction Generator by Means of Optimal Strategy," Energies, MDPI, vol. 13(3), pages 1-28, February.
    7. Ivorra, Benjamin & Mohammadi, Bijan & Manuel Ramos, Angel, 2015. "A multi-layer line search method to improve the initialization of optimization algorithms," European Journal of Operational Research, Elsevier, vol. 247(3), pages 711-720.
    8. Tanaka, Ken'ichiro & Toda, Alexis Akira, 2015. "Discretizing Distributions with Exact Moments: Error Estimate and Convergence Analysis," University of California at San Diego, Economics Working Paper Series qt7g23r5kh, Department of Economics, UC San Diego.
    9. Yasushi Narushima & Shummin Nakayama & Masashi Takemura & Hiroshi Yabe, 2023. "Memoryless Quasi-Newton Methods Based on the Spectral-Scaling Broyden Family for Riemannian Optimization," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 639-664, May.
    10. Ashrafi, M. & Khanjani, M.J. & Fadaei-Kermani, E. & Barani, G.A., 2015. "Farm drainage channel network optimization by improved modified minimal spanning tree," Agricultural Water Management, Elsevier, vol. 161(C), pages 1-8.
    11. Saha, Tanay & Rakshit, Suman & Khare, Swanand R., 2023. "Linearly structured quadratic model updating using partial incomplete eigendata," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    12. Sergey Badikov & Antoine Jacquier & Daphne Qing Liu & Patrick Roome, 2016. "No-arbitrage bounds for the forward smile given marginals," Papers 1603.06389, arXiv.org, revised Oct 2016.
    13. Szidarovszky, Ferenc & Luo, Yi, 2014. "Incorporating risk seeking attitude into defense strategy," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 104-109.
    14. Guang Li & Paat Rusmevichientong & Huseyin Topaloglu, 2015. "The d -Level Nested Logit Model: Assortment and Price Optimization Problems," Operations Research, INFORMS, vol. 63(2), pages 325-342, April.
    15. Zheng, Sanpeng & Feng, Renzhong, 2023. "A variable projection method for the general radial basis function neural network," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    16. Giorgio, 2019. "On Second-Order Optimality Conditions in Smooth Nonlinear Programming Problems," DEM Working Papers Series 171, University of Pavia, Department of Economics and Management.
    17. Jörg Fliege & Andrey Tin & Alain Zemkoho, 2021. "Gauss–Newton-type methods for bilevel optimization," Computational Optimization and Applications, Springer, vol. 78(3), pages 793-824, April.
    18. Csaba I. Fábián, 2021. "Gaining traction: on the convergence of an inner approximation scheme for probability maximization," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(2), pages 491-519, June.
    19. Hai-Jun Wang & Qin Ni, 2010. "A Convex Approximation Method For Large Scale Linear Inequality Constrained Minimization," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 27(01), pages 85-101.
    20. Milena J. Petrović & Ana Vučetić & Tanja Jovanović Spasojević, 2024. "Hybrid Modified Accelerated Gradient Method for Optimization Processes," Mathematics, MDPI, vol. 12(5), pages 1-13, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4411-:d:981214. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.