Počet záznamů: 1
On M-stationarity conditions in MPECs and the associated qualification conditions
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SYSNO ASEP 0474227 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název On M-stationarity conditions in MPECs and the associated qualification conditions Tvůrce(i) Adam, Lukáš (UTIA-B)
Henrion, R. (DE)
Outrata, Jiří (UTIA-B) RID, ORCIDCelkový počet autorů 3 Zdroj.dok. Mathematical Programming. - : Springer - ISSN 0025-5610
Roč. 168, 1-2 (2018), s. 229-259Poč.str. 31 s. Forma vydání Tištěná - P Jazyk dok. eng - angličtina Země vyd. NL - Nizozemsko Klíč. slova Mathematical programs with equilibrium constraints ; Optimality conditions ; Constraint qualification ; Calmness ; Perturbation mapping Vědní obor RIV BA - Obecná matematika Obor OECD Pure mathematics CEP GA15-00735S GA ČR - Grantová agentura ČR Institucionální podpora UTIA-B - RVO:67985556 UT WOS 000426071000010 EID SCOPUS 85017593151 DOI https://doi.org/10.1007/s10107-017-1146-3 Anotace 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. Pracoviště Ústav teorie informace a automatizace Kontakt Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Rok sběru 2019
Počet záznamů: 1