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A direct proof for M-stationarity under MPEC-GCQ for mathematical programs with equilibrium constraints

In: Optimization with Multivalued Mappings

Author

Listed:
  • Michael L. Flegel

    (University of Würzburg)

  • Christian Kanzow

    (University of Würzburg)

Abstract

Summary Mathematical programs with equilibrium constraints are optimization problems which violate most of the standard constraint qualifications. Hence the usual Karush-Kuhn-Tucker conditions cannot be viewed as first order optimality conditions unless relatively strong assumptions are satisfied. This observation has lead to a number of weaker first order conditions, with M-stationarity being the strongest among these weaker conditions. Here we show that M-stationarity is a first order optimality condition under a very weak Guignard-type constraint qualification. We present a short and direct approach.

Suggested Citation

  • Michael L. Flegel & Christian Kanzow, 2006. "A direct proof for M-stationarity under MPEC-GCQ for mathematical programs with equilibrium constraints," Springer Optimization and Its Applications, in: Stephan Dempe & Vyacheslav Kalashnikov (ed.), Optimization with Multivalued Mappings, pages 111-122, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-34221-4_6
    DOI: 10.1007/0-387-34221-4_6
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    Cited by:

    1. Lei Guo & Gui-Hua Lin, 2013. "Notes on Some Constraint Qualifications for Mathematical Programs with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 600-616, March.
    2. Jean-Pierre Dussault & Mounir Haddou & Abdeslam Kadrani & Tangi Migot, 2020. "On Approximate Stationary Points of the Regularized Mathematical Program with Complementarity Constraints," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 504-522, August.

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