On M-stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling
Please always quote using this URN:urn:nbn:de:0296-matheon-4002
- 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. Later 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: | Rene Henrion, Werner Römisch |
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URN: | urn:nbn:de:0296-matheon-4002 |
Referee: | Peter Imkeller |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2007/10/07 |
Release Date: | 2007/02/07 |
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Institute: | Humboldt-Universität zu Berlin |
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) | |
MSC-Classification: | 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C15 Stochastic programming |
Preprint Number: | 396 |