# MacEPEC

This page contains Sven and Todd's small collection or equilibrium problems with equilibrium constraints (EPECs). All models are written in AMPL. Each model has several formulations that are distinguished by their filename extensions:

Filename Extension | Formulation Type |
---|---|

GJ | Gauss-Jacobi formulation |

GS | Gauss-Seidel formulation |

MPEC | minimum multiplier formulation; mathematical program with equlilibrium constraints |

NCP | nonlinear complementarity problem formulation |

NCPa | alternative NCP formulation (complementarity between multipliers) |

NCPt | parametric NCP formulation |

NLP | elastic mode formulation; minimize complementarity |

PC | price-consistent (square) NCP formulation |

PCa | alternative price-consistent (square) NCP formulation |

**Updates:**

- 2006-04-27: corrected mistake in outrata4-GS/outrata4-GJ objective definition (now 10*y[4]^2)
- 2006-08-23: added data electric-004.dat which is a better conditioned example than electric-003.

#### electricity

A set of problems arising in the modeling of electricity markets.

- AllFirms.mod runs using electric-GJ.com for Gauss-Jacobi and electric-GS.com for Gauss-Seidel
- electric-MPEC.mod
- electric-NCP.mod
- electric-NCPa.mod
- electric-NCPt.mod runs using solve-NCPt.com
- electric-NLP.mod
- electric-PC.mod
- electric-PCa.mod

There are three data files for different networks:

- electric-001.dat a small 3 node
*infeasible*problem - electric-002.dat a small 3 node feasible problem
- electric-003.dat derived from an 18 node real example of the PJM market from the eastern United States
- electric-004.dat a made up example from the PJM example above that is better conditioned.

#### epecgen

A set of randomly generated EPECs. The random generator is written in matlab, see epecgen.m *

- EPEC-GJ.mod runs using solve-GJ.com
- EPEC.GS.mod runs using solve-GS.com
- EPEC-MPEC.mod
- EPEC-NCP.mod
- EPEC-NCPa.mod
- EPEC-NCPt.mod runs using solve-t.com
- EPEC-NLP.mod
- EPEC-PC.mod
- EPEC-PCa.mod

Sample data files are in three groups (different sizes):

- Size 1: 2 leaders with 8 variables and 4 constraints; 16 follower variables
- Size 2: 2 leaders with 16 variables and 8 constraints; 32 follower variables
- Size 3: 4 leaders with 16 variables and 8 constraints; 32 follower variables

#### ex-001

A small EPEC for which with a price-consistent formulations exists:

- ex-001-GJ.mod
- ex-001.GS.mod
- ex-001-MPEC.mod
- ex-001-NCP.mod
- ex-001-NCPa.mod
- ex-001-NCPt.mod
- ex-001-NLP.mod
- ex-001-PC.mod
- ex-001-PCa.mod

#### ex-4

A small EPEC from Fukushima and Pang which does not have a solution.

- ex-4-GJ.mod
- ex-4.GS.mod
- ex-4-MPEC.mod
- ex-4-NCP.mod
- ex-4-NCPa.mod
- ex-4-NCPt.mod
- ex-4-NLP.mod
- ex-4-PC.mod
- ex-4-PCa.mod

#### outrata3

An EPEC generated from the outrata3*.mod MPEC models. The control variables from all leaders enter the lower-level problem by averaging over the leaders. This trick ensures that the EPEC does not separate into individual MPECs. This problem has no solution and illustrates the behavior of the solvers when tackling a problem without solution. All Stackelberg players have the same constraints but different objective functions, so the problem has no price-consistent solution.

- outrata3-GJ.mod
- outrata3.GS.mod
- outrata3-MPEC.mod
- outrata3-NCP.mod
- outrata3-NCPa.mod
- outrata3-NCPt.mod
- outrata3-NLP.mod
- outrata3-PC.mod
- outrata3-PCa.mod

#### outrata4

This EPEC is derived from outrata3 so that a price-consistent solution to this model exists.

- outrata4-GJ.mod
- outrata4.GS.mod
- outrata4-MPEC.mod
- outrata4-NCP.mod
- outrata4-NCPa.mod
- outrata4-NCPt.mod
- outrata4-NLP.mod
- outrata4-PC.mod
- outrata4-PCa.mod