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