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On M-stationarity conditions in MPECs and the associated qualification conditions

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    0474227 - ÚTIA 2019 RIV NL eng J - Článek v odborném periodiku
    Adam, Lukáš - Henrion, R. - Outrata, Jiří
    On M-stationarity conditions in MPECs and the associated qualification conditions.
    Mathematical Programming. Roč. 168, 1-2 (2018), s. 229-259. ISSN 0025-5610. E-ISSN 1436-4646
    Grant CEP: GA ČR GA15-00735S
    Institucionální podpora: RVO:67985556
    Klíčová slova: Mathematical programs with equilibrium constraints * Optimality conditions * Constraint qualification * Calmness * Perturbation mapping
    Obor OECD: Pure mathematics
    Impakt faktor: 3.785, rok: 2018
    http://library.utia.cas.cz/separaty/2017/MTR/adam-0474227.pdf

    Depending on whether a mathematical program with equilibrium constraints (MPEC) is considered in its original or its enhanced (via KKT conditions) form, the assumed qualification conditions as well as the derived necessary optimality conditions may differ significantly. In this paper, we study this issue when imposing one of the weakest possible qualification conditions, namely the calmness of the perturbation mapping associated with the respective generalized equations in both forms of the MPEC. It is well known that the calmness property allows one to derive the so-called M-stationarity conditions. The restrictiveness of assumptions and the strength of conclusions in the two forms of theMPECis also strongly related to the qualification conditions on the “lower level”. For instance, even under the linear independence constraint qualification (LICQ) for a lower level feasible set described by C^1 functions, the calmness properties of the original and the enhanced perturbation mapping are drastically different. When passing to C^{1,1} data, this difference still remains true under the weaker Mangasarian–Fromovitz constraint qualification, whereas under LICQ both the calmness assumption and the derived optimality conditions are fully equivalent for the original and the enhanced form of the MPEC. After clarifying these relations, we provide a compilation of practically relevant consequences of our analysis in the derivation of necessary optimality conditions. The obtained results are finally applied to MPECs with structured equilibria.
    Trvalý link: http://hdl.handle.net/11104/0271365

     
     
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