Počet záznamů: 1  

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

  1. 1.
    SYSNO ASEP0474227
    Druh ASEPJ - Článek v odborném periodiku
    Zařazení RIVJ - Článek v odborném periodiku
    Poddruh JČlánek ve WOS
    NázevOn M-stationarity conditions in MPECs and the associated qualification conditions
    Tvůrce(i) Adam, Lukáš (UTIA-B)
    Henrion, R. (DE)
    Outrata, Jiří (UTIA-B) RID
    Celkový počet autorů3
    Zdroj.dok.Mathematical Programming. - : Springer - ISSN 0025-5610
    Roč. 168, 1-2 (2018), s. 229-259
    Poč.str.31 s.
    Forma vydáníTištěná - P
    Jazyk dok.eng - angličtina
    Země vyd.NL - Nizozemsko
    Klíč. slovaMathematical programs with equilibrium constraints ; Optimality conditions ; Constraint qualification ; Calmness ; Perturbation mapping
    Vědní obor RIVBA - Obecná matematika
    Obor OECDPure mathematics
    CEPGA15-00735S GA ČR - Grantová agentura ČR
    Institucionální podporaUTIA-B - RVO:67985556
    UT WOS000426071000010
    EID SCOPUS85017593151
    DOI10.1007/s10107-017-1146-3
    AnotaceDepending 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.
    PracovištěÚstav teorie informace a automatizace
    KontaktMarkéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201.
    Rok sběru2019
Počet záznamů: 1  

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