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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/GA15-00735S" target="_blank" >GA15-00735S: Stability analysis of optima and equilibria in economics</a><br>

Continuities

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

Publication year

2018

Confidentiality

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

Name of the periodical

Mathematical Programming

ISSN

0025-5610

e-ISSN

—

Volume of the periodical

168

Issue of the periodical within the volume

1-2

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

31

Pages from-to

229-259

UT code for WoS article

000426071000010

EID of the result in the Scopus database

2-s2.0-85017593151