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Analysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market∗

René Henrion; Jiří Outrata; Thomas Surowiec

ESAIM: Control, Optimisation and Calculus of Variations (2012)

  • Volume: 18, Issue: 2, page 295-317
  • ISSN: 1292-8119

Abstract

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We consider an equilibrium problem with equilibrium constraints (EPEC) arising from the modeling of competition in an electricity spot market (under ISO regulation). For a characterization of equilibrium solutions, so-called M-stationarity conditions are derived. This first requires a structural analysis of the problem, e.g., verifying constraint qualifications. Second, the calmness property of a certain multifunction has to be verified in order to justify using M-stationarity conditions. Third, for stating the stationarity conditions, the coderivative of a normal cone mapping has to be calculated. Finally, the obtained necessary conditions are made fully explicit in terms of the problem data for one typical constellation. A simple two-settlement example serves as an illustration.

How to cite

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Henrion, René, Outrata, Jiří, and Surowiec, Thomas. "Analysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market∗." ESAIM: Control, Optimisation and Calculus of Variations 18.2 (2012): 295-317. <http://eudml.org/doc/221922>.

@article{Henrion2012,
abstract = {We consider an equilibrium problem with equilibrium constraints (EPEC) arising from the modeling of competition in an electricity spot market (under ISO regulation). For a characterization of equilibrium solutions, so-called M-stationarity conditions are derived. This first requires a structural analysis of the problem, e.g., verifying constraint qualifications. Second, the calmness property of a certain multifunction has to be verified in order to justify using M-stationarity conditions. Third, for stating the stationarity conditions, the coderivative of a normal cone mapping has to be calculated. Finally, the obtained necessary conditions are made fully explicit in terms of the problem data for one typical constellation. A simple two-settlement example serves as an illustration. },
author = {Henrion, René, Outrata, Jiří, Surowiec, Thomas},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Equilibrium problems with equilibrium constraints; EPEC; M-stationary solutions; electricity spot market; calmness; equilibrium problems with equilibrium constraints},
language = {eng},
month = {7},
number = {2},
pages = {295-317},
publisher = {EDP Sciences},
title = {Analysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market∗},
url = {http://eudml.org/doc/221922},
volume = {18},
year = {2012},
}

TY - JOUR
AU - Henrion, René
AU - Outrata, Jiří
AU - Surowiec, Thomas
TI - Analysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market∗
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2012/7//
PB - EDP Sciences
VL - 18
IS - 2
SP - 295
EP - 317
AB - We consider an equilibrium problem with equilibrium constraints (EPEC) arising from the modeling of competition in an electricity spot market (under ISO regulation). For a characterization of equilibrium solutions, so-called M-stationarity conditions are derived. This first requires a structural analysis of the problem, e.g., verifying constraint qualifications. Second, the calmness property of a certain multifunction has to be verified in order to justify using M-stationarity conditions. Third, for stating the stationarity conditions, the coderivative of a normal cone mapping has to be calculated. Finally, the obtained necessary conditions are made fully explicit in terms of the problem data for one typical constellation. A simple two-settlement example serves as an illustration.
LA - eng
KW - Equilibrium problems with equilibrium constraints; EPEC; M-stationary solutions; electricity spot market; calmness; equilibrium problems with equilibrium constraints
UR - http://eudml.org/doc/221922
ER -

References

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