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

SYSNO ASEP	0474227
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	On M-stationarity conditions in MPECs and the associated qualification conditions
Author(s)	Adam, Lukáš (UTIA-B) Henrion, R. (DE) Outrata, Jiří (UTIA-B)_{RID, ORCID}
Number of authors	3
Source Title	Mathematical Programming. - : Springer - ISSN 0025-5610 Roč. 168, 1-2 (2018), s. 229-259
Number of pages	31 s.
Publication form	Print - P
Language	eng - English
Country	NL - Netherlands
Keywords	Mathematical programs with equilibrium constraints ; Optimality conditions ; Constraint qualification ; Calmness ; Perturbation mapping
Subject RIV	BA - General Mathematics
OECD category	Pure mathematics
R&D Projects	GA15-00735S GA ČR - Czech Science Foundation (CSF)
Institutional support	UTIA-B - RVO:67985556
UT WOS	000426071000010
EID SCOPUS	85017593151
DOI	10.1007/s10107-017-1146-3
Annotation	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.
Workplace	Institute of Information Theory and Automation
Contact	Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201.
Year of Publishing	2019

Number of the records: 1