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Optimality Conditions for Disjunctive Programs with Application to Mathematical Programs with Equilibrium Constraints

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Abstract

We consider optimization problems with a disjunctive structure of the feasible set. Using Guignard-type constraint qualifications for these optimization problems and exploiting some results for the limiting normal cone by Mordukhovich, we derive different optimality conditions. Furthermore, we specialize these results to mathematical programs with equilibrium constraints. In particular, we show that a new constraint qualification, weaker than any other constraint qualification used in the literature, is enough in order to show that a local minimum results in a so-called M-stationary point. Additional assumptions are also discussed which guarantee that such an M-stationary point is in fact a strongly stationary point.

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Authors and Affiliations

  1. Institute of Mathematics, University of Würzburg, Am Hubland, 97074, Würzburg, Germany

    Michael L. Flegel & Christian Kanzow

  2. Academy of Sciences, Institute of Information Theory and Automation, 18208, Prague, Czech Republic

    Jiří V. Outrata

Authors
  1. Michael L. Flegel
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  2. Christian Kanzow
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  3. Jiří V. Outrata
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Correspondence to Michael L. Flegel.

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Flegel, M.L., Kanzow, C. & Outrata, J.V. Optimality Conditions for Disjunctive Programs with Application to Mathematical Programs with Equilibrium Constraints. Set-Valued Anal 15, 139–162 (2007). https://doi.org/10.1007/s11228-006-0033-5

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  • DOI: https://doi.org/10.1007/s11228-006-0033-5

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