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A lifting method for generalized semi-infinite programs based on lower level Wolfe duality

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  • M. Diehl

    ()

  • B. Houska

    ()

  • O. Stein

    ()

  • P. Steuermann

    ()

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    Abstract

    This paper introduces novel numerical solution strategies for generalized semi-infinite optimization problems (GSIP), a class of mathematical optimization problems which occur naturally in the context of design centering problems, robust optimization problems, and many fields of engineering science. GSIPs can be regarded as bilevel optimization problems, where a parametric lower-level maximization problem has to be solved in order to check feasibility of the upper level minimization problem. The current paper discusses several strategies to reformulate this class of problems into equivalent finite minimization problems by exploiting the concept of Wolfe duality for convex lower level problems. Here, the main contribution is the discussion of the non-degeneracy of the corresponding formulations under various assumptions. Finally, these non-degenerate reformulations of the original GSIP allow us to apply standard nonlinear optimization algorithms. Copyright Springer Science+Business Media, LLC 2013

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    File URL: http://hdl.handle.net/10.1007/s10589-012-9489-4
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    Bibliographic Info

    Article provided by Springer in its journal Computational Optimization and Applications.

    Volume (Year): 54 (2013)
    Issue (Month): 1 (January)
    Pages: 189-210

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    Handle: RePEc:spr:coopap:v:54:y:2013:i:1:p:189-210

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    Web page: http://www.springer.com/math/journal/10589

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    Related research

    Keywords: Semi-infinite optimization; Lower level duality; Lifting approach; Adaptive convexification; Mathematical program with complementarity constraints;

    References

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    1. Stein, Oliver, 2012. "How to solve a semi-infinite optimization problem," European Journal of Operational Research, Elsevier, vol. 223(2), pages 312-320.
    2. Harald G├╝nzel & Hubertus Jongen & Oliver Stein, 2007. "On the closure of the feasible set in generalized semi-infinite programming," Central European Journal of Operations Research, Springer, vol. 15(3), pages 271-280, September.
    3. Gerhard-Wilhelm Weber & Aysun Tezel, 2007. "On generalized semi-infinite optimization of genetic networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 15(1), pages 65-77, July.
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