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An Improved Modification of Accelerated Double Direction and Double Step-Size Optimization Schemes

Author

Listed:
  • Milena J. Petrović

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

  • Dragana Valjarević

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

  • Dejan Ilić

    (Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18106 Niš, Serbia)

  • Aleksandar Valjarević

    (Faculty of Geography, University of Belgrade, Studentski Trg 3/III, 11000 Belgrade, Serbia)

  • Julija Mladenović

    (Faculty of Mathematics, University of Belgrade, Studentski Trg 16, 11000 Belgrade, Serbia)

Abstract

We propose an improved variant of the accelerated gradient optimization models for solving unconstrained minimization problems. Merging the positive features of either double direction, as well as double step size accelerated gradient models, we define an iterative method of a simpler form which is generally more effective. Performed convergence analysis shows that the defined iterative method is at least linearly convergent for uniformly convex and strictly convex functions. Numerical test results confirm the efficiency of the developed model regarding the CPU time, the number of iterations and the number of function evaluations metrics.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:2:p:259-:d:725397
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
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