# 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

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topHenrion, 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 -

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