0474227 20240103214018.420170427235959.9 85017593151 000426071000010 10.1007/s10107-017-1146-3 31 s. P cav_un_epca*02572270025-5610168229-259Springer Mathematical programs with equilibrium constraints Optimality conditions Constraint qualification Calmness Perturbation mapping cav_un_auth*0309054 Adam Lukáš Matematická teorie rozhodování Department of Decision Making Theory MTR MTR UTIA-B Department of Decision Making Theory CZ Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0015558 Henrion R. DE cav_un_auth*0101173 Outrata Jiří Matematická teorie rozhodování Department of Decision Making Theory MTR MTR UTIA-B Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2017/MTR/adam-0474227.pdf cav_un_auth*0321507 GA15-00735S GA ČR 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. WOS BA 10000 10100 10101 2019 3 4 A hod 4ah 20231122142418.0 RVO:67985556 http://hdl.handle.net/11104/0271365 cav_un_auth*0305285 Weierstraß-Institut für Angewandte Analysis und Stochastik DE 1 Department of Decision Making Theory UTIA-B 10102 MATHEMATICS, APPLIED S 2 Article Computer Science Software Engineering|Operations Research Management Science|Mathematics Applied COMPUTERSCIENCE.SOFTWAREENGINEERING|OPERATIONSRESEARCH&MANAGEMENTSCIENCE|MATHEMATICS.APPLIED 4.028 1.234 14.1 0.02247 2.961 10771 2.853 3.571 124 Q1 98.58 90.8 Q1* Q1* 1.9 Q1 97.441 2018 Soubory v repozitáři: adam-0474227.pdf 85017593151 SCOPUS PUBMED 000426071000010 WOS cav_un_epca*0257227 Mathematical Programming 0025-5610 1436-4646 Roč. 168 1-2 2018 229 259 Springer