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Semi-continuous quadratic optimization: existence conditions and duality scheme

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Abstract

In this work, we study the class of problems called semi-continuous optimization, which contains constrained minimization (maximization) problems with lower (upper) semi-continuous objective functions. We show some existence conditions for solutions based on asymptotic techniques, as well as a duality scheme based on the Fenchel–Moreau conjugation specifically applied to semi-continuous problems. Promising results are obtained, when we apply this scheme to minimize quadratic functions (whose Hessians can be symmetric indefinite) over nonempty, closed and convex polyhedral sets.

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Acknowledgments

The authors are thankful for the valuable suggestions given by the anonymous referees that improved the paper. Fernanda Raupp was partially supported by FAPERJ/CNPq through PRONEX 662199/2010-12 and CNPq Grant 311165/2013-3, whereas Wilfredo Sosa was partially supported by CNPq Grants 302074/2012-0 and 471168/2013-0.

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Authors and Affiliations

  1. Universidad del Pacífico, Lima, Peru

    John Cotrina

  2. Departamento de Engenharia Industrial, Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, Brazil

    Fernanda M. P. Raupp

  3. Laboratório Nacional de Computação Científica, Petrópolis, Brazil

    Fernanda M. P. Raupp

  4. Programa de Pós-Graduação em Economia, Universidade Católica de Brasília, Brasília, Brazil

    Wilfredo Sosa

Authors
  1. John Cotrina
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  2. Fernanda M. P. Raupp
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  3. Wilfredo Sosa
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Correspondence to Fernanda M. P. Raupp.

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Cotrina, J., Raupp, F.M.P. & Sosa, W. Semi-continuous quadratic optimization: existence conditions and duality scheme. J Glob Optim 63, 281–295 (2015). https://doi.org/10.1007/s10898-015-0306-3

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  • DOI: https://doi.org/10.1007/s10898-015-0306-3

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