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An inexact restoration approach to optimization problems with multiobjective constraints under weighted-sum scalarization

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Abstract

We apply a flexible inexact-restoration (IR) algorithm to optimization problems with multiobjective constraints under the weighted-sum scalarization approach. In IR methods each iteration has two phases. In the first phase one aims to improve the feasibility and, in the second phase, one minimizes a suitable objective function. We show that with the IR framework there is a natural way to explore the structure of the problem in both IR phases. Numerical experiments are conducted on Portfolio optimization, the Moré–Garbow–Hillstrom collection, and random fourth-degree polynomials, where we show the advantages of exploiting the structure of the problem.

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Acknowledgments

This work was supported by PRONEX-CNPq/FAPERJ Grant E-26/171.164/2003-APQ1, FAPESP Grants 2010/19720-5, 2013/05475-7, 2014/01446-5 and 2015/02528-8, CEPID-Cemeai-Fapesp Industrial Mathematics 201307375-0, and CNPq. We would like to thank the anonymous referees for insightful comments and suggestions.

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Authors and Affiliations

  1. Institute of Science and Technology, Federal University of São Paulo, São José dos Campos, SP, Brazil

    L. F. Bueno

  2. Department of Applied Mathematics, Institute of Mathematics and Statistics, University of São Paulo, São Paulo, SP, Brazil

    G. Haeser

  3. Department of Applied Mathematics Institute of Mathematics, Statistics and Scientific Computing, University of Campinas, Campinas, SP, Brazil

    J. M. Martínez

Authors
  1. L. F. Bueno
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  2. G. Haeser
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  3. J. M. Martínez
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Correspondence to G. Haeser.

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Bueno, L.F., Haeser, G. & Martínez , J.M. An inexact restoration approach to optimization problems with multiobjective constraints under weighted-sum scalarization. Optim Lett 10, 1315–1325 (2016). https://doi.org/10.1007/s11590-015-0928-x

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  • DOI: https://doi.org/10.1007/s11590-015-0928-x

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