On M -stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling

René Henrion; Werner Römisch

Applications of Mathematics (2007)

  • Volume: 52, Issue: 6, page 473-494
  • ISSN: 0862-7940

Abstract

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Modeling several competitive leaders and followers acting in an electricity market leads to coupled systems of mathematical programs with equilibrium constraints, called equilibrium problems with equilibrium constraints (EPECs). We consider a simplified model for competition in electricity markets under uncertainty of demand in an electricity network as a (stochastic) multi-leader-follower game. First order necessary conditions are developed for the corresponding stochastic EPEC based on a result of Outrata. For applying the general result an explicit representation of the co-derivative of the normal cone mapping to a polyhedron is derived. Then the co-derivative formula is used for verifying constraint qualifications and for identifying M -stationary solutions of the stochastic EPEC if the demand is represented by a finite number of scenarios.

How to cite

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Henrion, René, and Römisch, Werner. "On $M$-stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling." Applications of Mathematics 52.6 (2007): 473-494. <http://eudml.org/doc/33304>.

@article{Henrion2007,
abstract = {Modeling several competitive leaders and followers acting in an electricity market leads to coupled systems of mathematical programs with equilibrium constraints, called equilibrium problems with equilibrium constraints (EPECs). We consider a simplified model for competition in electricity markets under uncertainty of demand in an electricity network as a (stochastic) multi-leader-follower game. First order necessary conditions are developed for the corresponding stochastic EPEC based on a result of Outrata. For applying the general result an explicit representation of the co-derivative of the normal cone mapping to a polyhedron is derived. Then the co-derivative formula is used for verifying constraint qualifications and for identifying $M$-stationary solutions of the stochastic EPEC if the demand is represented by a finite number of scenarios.},
author = {Henrion, René, Römisch, Werner},
journal = {Applications of Mathematics},
keywords = {electricity markets; bidding; noncooperative games; equilibrium constraint; EPEC; optimality condition; co-derivative; random demand; electricity markets; bidding; noncooperative games; equilibrium constraint; EPEC; optimality condition},
language = {eng},
number = {6},
pages = {473-494},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On $M$-stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling},
url = {http://eudml.org/doc/33304},
volume = {52},
year = {2007},
}

TY - JOUR
AU - Henrion, René
AU - Römisch, Werner
TI - On $M$-stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling
JO - Applications of Mathematics
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 6
SP - 473
EP - 494
AB - Modeling several competitive leaders and followers acting in an electricity market leads to coupled systems of mathematical programs with equilibrium constraints, called equilibrium problems with equilibrium constraints (EPECs). We consider a simplified model for competition in electricity markets under uncertainty of demand in an electricity network as a (stochastic) multi-leader-follower game. First order necessary conditions are developed for the corresponding stochastic EPEC based on a result of Outrata. For applying the general result an explicit representation of the co-derivative of the normal cone mapping to a polyhedron is derived. Then the co-derivative formula is used for verifying constraint qualifications and for identifying $M$-stationary solutions of the stochastic EPEC if the demand is represented by a finite number of scenarios.
LA - eng
KW - electricity markets; bidding; noncooperative games; equilibrium constraint; EPEC; optimality condition; co-derivative; random demand; electricity markets; bidding; noncooperative games; equilibrium constraint; EPEC; optimality condition
UR - http://eudml.org/doc/33304
ER -

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Citations in EuDML Documents

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  1. René Henrion, Jiří Outrata, Thomas Surowiec, A note on the relation between strong and M-stationarity for a class of mathematical programs with equilibrium constraints
  2. René Henrion, Jiří Outrata, Thomas Surowiec, Analysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market
  3. René Henrion, Jiří Outrata, Thomas Surowiec, Analysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market

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