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

Michael L. Flegel () and Christian Kanzow ()
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Michael L. Flegel: University of Würzburg
Christian Kanzow: University of Würzburg

A chapter in Optimization with Multivalued Mappings, 2006, pp 111-122 from Springer

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.

Keywords: Mathematical programs with equilibrium constraints; M-stationarity; Guignard constraint qualification (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-0-387-34221-4_6

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DOI: 10.1007/0-387-34221-4_6

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