Analysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market
- Henrion, René
- Outrata, Jiří
- Surowiec, Thomas
2010 Mathematics Subject Classification
- 90C30 49J53
- Equilibrium problems with equilibrium constraints, EPEC, $M$-stationary solutions, electricity spot market, calmness
We consider an equilibrium problem with equilibrium constraints (EPEC) as it arises from modeling competition in an electricity spot market (under ISO regulation). For a characterization of equilibrium solutions, so-called $M$-stationarity conditions are derived. This requires a structural analysis of the problem first (constraint qualifications, strong regularity). Second, the calmness property of a certain multifunction has to be verified in order to justify $M$-stationarity. Third, for stating the stationarity conditions, the co-derivative 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-settlements example serves as an illustration.
- ESAIM Control Optim. Calc. Var., 18 (2012) pp. 295--317.