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

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  • 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
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    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, December.
    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, March.
    6. Neculai Andrei, 2020. "Nonlinear Conjugate Gradient Methods for Unconstrained Optimization," Springer Optimization and Its Applications, Springer, number 978-3-030-42950-8, March.
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