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A DIRECT-type approach for derivative-free constrained global optimization

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Abstract

In the field of global optimization, many efforts have been devoted to globally solving bound constrained optimization problems without using derivatives. In this paper we consider global optimization problems where both bound and general nonlinear constraints are present. To solve this problem we propose the combined use of a DIRECT-type algorithm with a derivative-free local minimization of a nonsmooth exact penalty function. In particular, we define a new DIRECT-type strategy to explore the search space by explicitly taking into account the two-fold nature of the optimization problems, i.e. the global optimization of both the objective function and of a feasibility measure. We report an extensive experimentation on hard test problems to show viability of the approach.

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Acknowledgments

This work has been partially funded by the UE (ENIAC Joint Undertaking) in the MODERN project (ENIAC-120003).

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Authors and Affiliations

  1. Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti”, Consiglio Nazionale delle Ricerche, Via dei Taurini 19, 00185, Rome, Italy

    G. Liuzzi

  2. Department of Computer, Control and Management Engineering, “Sapienza” University of Rome, via Ariosto 25, 00185, Rome, Italy

    G. Di Pillo & S. Lucidi

  3. Dipartimento di Ingegneria Civile e Ingegneria Informatica, Università degli Studi di Roma “Tor Vergata”, Viale del Politecnico 1, 00133, Rome, Italy

    V. Piccialli

  4. Dipartimento di Matematica, Università di Padova, Via Trieste 63, 35121, Padua, Italy

    F. Rinaldi

Authors
  1. G. Di Pillo
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  2. G. Liuzzi
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  3. S. Lucidi
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  4. V. Piccialli
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  5. F. Rinaldi
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Correspondence to F. Rinaldi.

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Di Pillo, G., Liuzzi, G., Lucidi, S. et al. A DIRECT-type approach for derivative-free constrained global optimization. Comput Optim Appl 65, 361–397 (2016). https://doi.org/10.1007/s10589-016-9876-3

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