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Regularized optimization methods for convex MINLP problems

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Abstract

We propose regularized cutting-plane methods for solving mixed-integer nonlinear programming problems with nonsmooth convex objective and constraint functions. The given methods iteratively search for trial points in certain localizer sets, constructed by employing linearizations of the involved functions. New trial points can be chosen in several ways; for instance, by minimizing a regularized cutting-plane model if functions are costly. When dealing with hard-to-evaluate functions, the goal is to solve the optimization problem by performing as few function evaluations as possible. Numerical experiments comparing the proposed algorithms with classical methods in this area show the effectiveness of our approach.

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Notes

  1. The notation \(f^+\) stands for \(f^+(x)=\max \{f(x),0\}\).

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Acknowledgments

The author gratefully acknowledges financial support provided by Severo Ochoa Program SEV-2013-0323 and Basque Government BERC Program 2014-2017. The author also thanks the associate editor and two anonymous referees for their constructive suggestions that considerably improved the original version of this article.

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Authors and Affiliations

  1. UERJ, Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil

    Welington de Oliveira

  2. BCAM, Basque Center for Applied Mathematics, Alameda de Mazarredo, 14, 48009, Bilbao, Basque Country, Spain

    Welington de Oliveira

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  1. Welington de Oliveira
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Correspondence to Welington de Oliveira.

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de Oliveira, W. Regularized optimization methods for convex MINLP problems. TOP 24, 665–692 (2016). https://doi.org/10.1007/s11750-016-0413-4

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