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A New Descent Algorithm Using the Three-Step Discretization Method for Solving Unconstrained Optimization Problems

Author

Listed:
  • Mina Torabi

    (Department of Applied Mathematics, Faculty of Mathematics, Yazd University, P. O. Box 89195-741, Yazd, Iran)

  • Mohammad-Mehdi Hosseini

    (Department of Applied Mathematics, Faculty of Mathematics, Yazd University, P. O. Box 89195-741, Yazd, Iran)

Abstract

In this paper, three-step Taylor expansion, which is equivalent to third-order Taylor expansion, is used as a mathematical base of the new descent method. At each iteration of this method, three steps are performed. Each step has a similar structure to the steepest descent method, except that the generalized search direction, step length, and next iterative point are applied. Compared with the steepest descent method, it is shown that the proposed algorithm has higher convergence speed and lower computational cost and storage.

Suggested Citation

  • Mina Torabi & Mohammad-Mehdi Hosseini, 2018. "A New Descent Algorithm Using the Three-Step Discretization Method for Solving Unconstrained Optimization Problems," Mathematics, MDPI, vol. 6(4), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:4:p:63-:d:142570
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    References listed on IDEAS

    as
    1. Kaori Sugiki & Yasushi Narushima & Hiroshi Yabe, 2012. "Globally Convergent Three-Term Conjugate Gradient Methods that Use Secant Conditions and Generate Descent Search Directions for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 733-757, June.
    2. Vieira, Douglas Alexandre Gomes & Lisboa, Adriano Chaves, 2014. "Line search methods with guaranteed asymptotical convergence to an improving local optimum of multimodal functions," European Journal of Operational Research, Elsevier, vol. 235(1), pages 38-46.
    3. Clóvis Gonzaga & Ruana Schneider, 2016. "On the steepest descent algorithm for quadratic functions," Computational Optimization and Applications, Springer, vol. 63(2), pages 523-542, March.
    Full references (including those not matched with items on IDEAS)

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