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Immunizing Conic Quadratic Optimization Problems Against Implementation Errors

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  • Ben-Tal, A.
  • Hertog, D. den

    (Tilburg University, Center for Economic Research)

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    Abstract

    We show that the robust counterpart of a convex quadratic constraint with ellipsoidal implementation error is equivalent to a system of conic quadratic constraints. To prove this result we first derive a sharper result for the S-lemma in case the two matrices involved can be simultaneously diagonalized. This extension of the S-lemma may also be useful for other purposes. We extend the result to the case in which the uncertainty region is the intersection of two convex quadratic inequalities. The robust counterpart for this case is also equivalent to a system of conic quadratic constraints. Results for convex conic quadratic constraints with implementation error are also given. We conclude with showing how the theory developed can be applied in robust linear optimization with jointly uncertain parameters and implementation errors, in sequential robust quadratic programming, in Taguchi’s robust approach, and in the adjustable robust counterpart.

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    Bibliographic Info

    Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2011-060.

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    Date of creation: 2011
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    Handle: RePEc:dgr:kubcen:2011060

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

    Related research

    Keywords: Conic Quadratic Program; hidden convexity; implementation error; robust optimization; simultaneous diagonalizability; S-lemma;

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    References

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    1. Stinstra, Erwin & den Hertog, Dick, 2008. "Robust optimization using computer experiments," European Journal of Operational Research, Elsevier, vol. 191(3), pages 816-837, December.
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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.
    2. Gabrel, Virginie & Murat, Cécile & Thiele, Aurélie, 2014. "Recent advances in robust optimization: An overview," European Journal of Operational Research, Elsevier, vol. 235(3), pages 471-483.
    3. Ben-Tal, A. & Hertog, D. den & Laurent, M., 2011. "Hidden Convexity in Partially Separable Optimization," Discussion Paper 2011-070, Tilburg University, Center for Economic Research.

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