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A New Method for Deriving Robust and Globalized Robust Solutions of Uncertain Linear Conic Optimization Problems Having General Convex Uncertainty Sets


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  • Gorissen, B.L.
  • Ben-Tal, A.
  • Blanc, J.P.C.
  • Hertog, D. den

    (Tilburg University, Center for Economic Research)


Abstract: We propose a new way to derive tractable robust counterparts of a linear conic optimization problem by using the theory of Beck and Ben-Tal [2] on the duality between the robust (“pessimistic”) primal problem and its “optimistic” dual. First, we obtain a new convex reformulation of the dual problem of a robust linear conic program, and then show how to construct the primal robust solution from the dual optimal solution. Our result allows many new uncertainty regions to be considered. We give examples of tractable uncertainty regions that were previously intractable. The results are illustrated by solving a multi-item newsvendor problem. We also propose a new globalized robust counterpart that is more flexible, and is tractable for general convex uncertainty sets and any convex distance function.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2012-076.

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Date of creation: 2012
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Handle: RePEc:dgr:kubcen:2012076

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Keywords: robust optimization; general convex uncertainty regions; linear conic optimization;

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  1. Ben-Tal, A. & Hertog, D. den & De Waegenaere, A.M.B. & Melenberg, B. & Rennen, G., 2011. "Robust Solutions of Optimization Problems Affected by Uncertain Probabilities," Discussion Paper 2011-061, Tilburg University, Center for Economic Research.
  2. Blanc, J.P.C. & Hertog, D. den, 2008. "On Markov Chains with Uncertain Data," Discussion Paper 2008-50, Tilburg University, Center for Economic Research.
  3. 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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Cited by:
  1. Gorissen, B.L. & Yanikoglu, I. & Hertog, D. den, 2013. "Hints for practical robust optimization," Discussion Paper 2013-065, 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.


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