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Hidden Convexity in Partially Separable Optimization

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  • Ben-Tal, A.
  • Hertog, D. den
  • Laurent, M.

    (Tilburg University, Center for Economic Research)

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    Abstract

    The paper identifies classes of nonconvex optimization problems whose convex relaxations have optimal solutions which at the same time are global optimal solutions of the original nonconvex problems. Such a hidden convexity property was so far limited to quadratically constrained quadratic problems with one or two constraints. We extend it here to problems with some partial separable structure. Among other things, the new hidden convexity results open up the possibility to solve multi-stage robust optimization problems using certain nonlinear decision rules.

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    Bibliographic Info

    Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2011-070.

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    Date of creation: 2011
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    Handle: RePEc:dgr:kubcen:2011070

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    Web page: http://center.uvt.nl

    Related research

    Keywords: convex relaxation of nonconvex problems; hidden convexity; partially separable functions; robust optimization;

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    1. Aharon Ben-Tal & Dick den Hertog & Anja De Waegenaere & Bertrand Melenberg & Gijs Rennen, 2013. "Robust Solutions of Optimization Problems Affected by Uncertain Probabilities," Management Science, INFORMS, vol. 59(2), pages 341-357, April.
    2. Ben-Tal, A. & Hertog, D. den, 2011. "Immunizing Conic Quadratic Optimization Problems Against Implementation Errors," Discussion Paper 2011-060, Tilburg University, Center for Economic Research.
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    Cited by:
    1. Ben-Tal, A. & Hertog, D. den & Vial, J.P., 2012. "Deriving Robust Counterparts of Nonlinear Uncertain Inequalities," Discussion Paper 2012-053, Tilburg University, Center for Economic Research.

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