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A class of derivative-free nonmonotone optimization algorithms employing coordinate rotations and gradient approximations

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  • L. Grippo
  • F. Rinaldi

Abstract

In this paper we study a class of derivative-free unconstrained minimization algorithms employing nonmonotone inexact linesearch techniques along a set of suitable search directions. In particular, we define globally convergent nonmonotone versions of some well-known derivative-free methods and we propose a new linesearch-based nonmonotone algorithm, where search directions are constructed by combining coordinate rotations with simplex gradients. Through extensive numerical experimentation, we show that the proposed algorithm is highly competitive in comparison with some of the most efficient direct search methods and model based methods on a large set of test problems. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • L. Grippo & F. Rinaldi, 2015. "A class of derivative-free nonmonotone optimization algorithms employing coordinate rotations and gradient approximations," Computational Optimization and Applications, Springer, vol. 60(1), pages 1-33, January.
    • Handle: RePEc:spr:coopap:v:60:y:2015:i:1:p:1-33
    DOI: 10.1007/s10589-014-9665-9
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    References listed on IDEAS

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    1. G. Liuzzi & S. Lucidi & F. Rinaldi, 2012. "Derivative-free methods for bound constrained mixed-integer optimization," Computational Optimization and Applications, Springer, vol. 53(2), pages 505-526, October.
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    Cited by:

    1. Milagros Loreto & Hugo Aponte & Debora Cores & Marcos Raydan, 2017. "Nonsmooth spectral gradient methods for unconstrained optimization," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(4), pages 529-553, December.
    2. László Pál, 2017. "Empirical study of the improved UNIRANDI local search method," 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. 25(4), pages 929-952, December.
    3. Jingyong Tang & Jinchuan Zhou & Zhongfeng Sun, 2023. "A derivative-free line search technique for Broyden-like method with applications to NCP, wLCP and SI," Annals of Operations Research, Springer, vol. 321(1), pages 541-564, February.

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