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

Identifikátory výsledku

  • Kód výsledku v IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F18%3A00474227" target="_blank" >RIV/67985556:_____/18:00474227 - isvavai.cz</a>

  • Výsledek na webu

    <a href="http://dx.doi.org/10.1007/s10107-017-1146-3" target="_blank" >http://dx.doi.org/10.1007/s10107-017-1146-3</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1007/s10107-017-1146-3" target="_blank" >10.1007/s10107-017-1146-3</a>

Alternativní jazyky

  • Jazyk výsledku

    angličtina

  • Název v původním jazyce

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

  • Popis výsledku v původním jazyce

    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.

  • Název v anglickém jazyce

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

  • Popis výsledku anglicky

    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.

Klasifikace

  • Druh

    J<sub>imp</sub> - Článek v periodiku v databázi Web of Science

  • CEP obor

  • OECD FORD obor

    10101 - Pure mathematics

Návaznosti výsledku

  • Projekt

    <a href="/cs/project/GA15-00735S" target="_blank" >GA15-00735S: Analýza stability optim a ekvilibrií v ekonomii</a><br>

  • Návaznosti

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Ostatní

  • Rok uplatnění

    2018

  • Kód důvěrnosti údajů

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Údaje specifické pro druh výsledku

  • Název periodika

    Mathematical Programming

  • ISSN

    0025-5610

  • e-ISSN

  • Svazek periodika

    168

  • Číslo periodika v rámci svazku

    1-2

  • Stát vydavatele periodika

    NL - Nizozemsko

  • Počet stran výsledku

    31

  • Strana od-do

    229-259

  • Kód UT WoS článku

    000426071000010

  • EID výsledku v databázi Scopus

    2-s2.0-85017593151