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An interval branch and bound method for global Robust optimization

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Abstract

In this paper, we design a Branch and Bound algorithm based on interval arithmetic to address nonconvex robust optimization problems. This algorithm provides the exact global solution of such difficult problems arising in many real life applications. A code was developed in MatLab and was used to solve some robust nonconvex problems with few variables. This first numerical study shows the interest of this approach providing the global solution of such difficult robust nonconvex optimization problems.

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Notes

  1. An interval function F is said isotone if for any couple \((X',X)\) such that \(X'\subseteq X\), we have \(F(X')\subseteq F(X)\).

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Authors and Affiliations

  1. IMUS-Instituto de Matemáticas de la Universidad de Sevilla, Sevilla, Spain

    Emilio Carrizosa

  2. Université de Toulouse, LAPLACE (CNRS UMR5213), ENSEEIHT-Toulouse INP, Toulouse, France

    Frédéric Messine

Authors
  1. Emilio Carrizosa
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  2. Frédéric Messine
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Correspondence to Frédéric Messine.

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The work of E. Carrizosa has been funded in part by Projects MTM2015-65915-R (Ministerio de Ciencia e Innovación, Spain), P11-FQM-7603, FQM329 (Junta de Andalucía), all with EU ERDF funds.

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Carrizosa, E., Messine, F. An interval branch and bound method for global Robust optimization. J Glob Optim 80, 507–522 (2021). https://doi.org/10.1007/s10898-021-01010-5

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  • DOI: https://doi.org/10.1007/s10898-021-01010-5

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