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

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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.

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Acknowledgments

The authors would like to thank the anonymous reviewers for their helpful and constructive comments that greatly contributed to improve the paper.

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Authors and Affiliations

  1. Dipartimento di Ingegneria Informatica Automatica e Gestionale, “Sapienza” University of Rome, Rome, Italy

    L. Grippo

  2. Dipartimento di Matematica, University of Padua, Padua, Italy

    F. Rinaldi

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  1. L. Grippo
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  2. F. Rinaldi
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Correspondence to F. Rinaldi.

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Grippo, L., Rinaldi, F. A class of derivative-free nonmonotone optimization algorithms employing coordinate rotations and gradient approximations. Comput Optim Appl 60, 1–33 (2015). https://doi.org/10.1007/s10589-014-9665-9

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  • DOI: https://doi.org/10.1007/s10589-014-9665-9

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