Difference between revisions of "MacEPEC"

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This page contains [http://www.mcs.anl.gov/~leyffer/  Sven] and [http://www.mcs.anl.gov/~tmunson/ Todd]'s small collection or equilibrium problems with equilibrium constraints (EPECs). All models are written in [http://www.ampl.com/ AMPL]. Each model has several formulations that are distinguished by their filename extensions:
 
This page contains [http://www.mcs.anl.gov/~leyffer/  Sven] and [http://www.mcs.anl.gov/~tmunson/ Todd]'s small collection or equilibrium problems with equilibrium constraints (EPECs). All models are written in [http://www.ampl.com/ AMPL]. Each model has several formulations that are distinguished by their filename extensions:
  
−
{| width="100%" border="1" cellpadding="0" cellspacing="0"
+
{| border="1" cellpadding="0" cellspacing="0"
−
| width="21%" | Filename Extension
+
|- align="left"
−
| width="79%" | Formulation Type
+
! Filename Extension
 +
! Formulation Type
 
|-
 
|-
−
| width="21%" | GJ
+
| GJ
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| width="79%" | Gauss-Jacobi formulation
+
| Gauss-Jacobi formulation
 
|-
 
|-
−
| width="21%" | GS
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| GS
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| width="79%" | Gauss-Seidel formulation
+
| Gauss-Seidel formulation
 
|-
 
|-
−
| width="21%" | MPEC
+
| MPEC
−
| width="79%" | minimum multiplier formulation; mathematical program with equlilibrium constraints
+
| minimum multiplier formulation; mathematical program with equlilibrium constraints
 
|-
 
|-
−
| width="21%" | NCP
+
| NCP
−
| width="79%" | nonlinear complementarity problem formulation
+
| nonlinear complementarity problem formulation
 
|-
 
|-
−
| width="21%" | NCPa
+
| NCPa
−
| width="79%" | alternative NCP formulation (complementarity between multipliers)
+
| alternative NCP formulation (complementarity between multipliers)
 
|-
 
|-
−
| width="21%" | NCPt
+
| NCPt
−
| width="79%" | parametric NCP formulation
+
| parametric NCP formulation
 
|-
 
|-
−
| width="21%" | NLP
+
| NLP
−
| width="79%" | elastic mode formulation; minimize complementarity
+
| elastic mode formulation; minimize complementarity
 
|-
 
|-
−
| width="21%" | PC
+
| PC
−
| width="79%" | price-consistent (square) NCP formulation
+
| price-consistent (square) NCP formulation
 
|-
 
|-
−
| width="21%" | PCa
+
| PCa
−
| width="79%" | alternative price-consistent (square) NCP formulation
+
| alternative price-consistent (square) NCP formulation
 
|}
 
|}
  
−
----
+
'''Updates:'''
−
 
 
−
Updates:
 
  
 
# 2006-04-27: corrected mistake in outrata4-GS/outrata4-GJ objective definition (now 10*y[4]^2)
 
# 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.
 
# 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.  
−
electricity a set of problems arising in the modeling of electricity markets.  
+
* [http://www.mcs.anl.gov/~leyffer/macepec/AllFirms.mod AllFirms.mod] runs using [http://www.mcs.anl.gov/~leyffer/macepec/electric-GJ.com electric-GJ.com] for Gauss-Jacobi and [http://www.mcs.anl.gov/~leyffer/macepec/electric-GS.com electric-GS.com] for Gauss-Seidel  
−
 
+
* [http://www.mcs.anl.gov/~leyffer/macepec/electric-MPEC.mod electric-MPEC.mod]   
−
<blockquote>
+
* [http://www.mcs.anl.gov/~leyffer/macepec/electric-NCP.mod electric-NCP.mod]  
−
 
+
* [http://www.mcs.anl.gov/~leyffer/macepec/electric-NCPa.mod electric-NCPa.mod]
−
AllFirms.mod runs using electric-GJ.com for Gauss-Jacobi and electric-GS.com for Gauss-Seidel [electric-MPEC.mod <br />electric-MPEC.mod] [electric-NCP.mod <br />electric-NCP.mod]  [electric-NCPa.mod <br />electric-NCPa.mod]  [electric-NCPt.mod <br />electric-NCPt.mod] runs using solve-NCPt.com  [electric-NLP.mod <br />electric-NLP.mod] [electric-PC.mod <br />electric-PC.mod] <br />electric-PCa.mod  
+
* [http://www.mcs.anl.gov/~leyffer/macepec/electric-NCPt.mod electric-NCPt.mod] runs using [http://www.mcs.anl.gov/~leyffer/macepec/solve-NCPt.com solve-NCPt.com]
−
 
+
* [http://www.mcs.anl.gov/~leyffer/macepec/electric-NLP.mod electric-NLP.mod]   
−
</blockquote>
+
* [http://www.mcs.anl.gov/~leyffer/macepec/electric-PC.mod electric-PC.mod]
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/electric-PCa.mod electric-PCa.mod]
  
 
There are three data files for different networks:
 
There are three data files for different networks:
 +
# [http://www.mcs.anl.gov/~leyffer/macepec/electric-001.dat electric-001.dat] a small 3 node ''infeasible'' problem
 +
# [http://www.mcs.anl.gov/~leyffer/macepec/electric-002.dat electric-002.dat] a small 3 node feasible problem
 +
# [http://www.mcs.anl.gov/~leyffer/macepec/electric-003.dat electric-003.dat] derived from an 18 node real example of the PJM market from the eastern United States
 +
# [http://www.mcs.anl.gov/~leyffer/macepec/electric-004.dat electric-004.dat] a made up example from the PJM example above that is better conditioned.
  
−
<blockquote>
+
==== epecgen ====
−
 
+
A set of randomly generated EPECs. The random generator is written in matlab, see epecgen.m *
−
electric-001.dat a small 3 node ''infeasible'' problem <br />electric-002.dat a small 3 node feasible problem<br />electric-003.dat derived from an 18 node real example of the [pjm.jpg PJM market] from the eastern United States<br />electric-004.dat a made up example from the PJM example above that is better conditioned.
+
* [http://www.mcs.anl.gov/~leyffer/macepec/EPEC-GJ.mod EPEC-GJ.mod] runs using solve-GJ.com
−
 
+
* [http://www.mcs.anl.gov/~leyffer/macepec/EPEC-GS.mod EPEC.GS.mod] runs using solve-GS.com
−
</blockquote>
+
* [http://www.mcs.anl.gov/~leyffer/macepec/EPEC-MPEC.mod EPEC-MPEC.mod]
−
----
+
* [http://www.mcs.anl.gov/~leyffer/macepec/EPEC-NCP.mod EPEC-NCP.mod]
−
 
+
* [http://www.mcs.anl.gov/~leyffer/macepec/EPEC-NCPa.mod EPEC-NCPa.mod]
−
epecgen a set of randomly generated EPECs. The random generator is written in matlab, see epecgen.m  
+
* [http://www.mcs.anl.gov/~leyffer/macepec/EPEC-NCPt.mod EPEC-NCPt.mod] runs using solve-t.com
−
 
+
* [http://www.mcs.anl.gov/~leyffer/macepec/EPEC-NLP.mod EPEC-NLP.mod]
−
<blockquote>
+
* [http://www.mcs.anl.gov/~leyffer/macepec/EPEC-PC.mod EPEC-PC.mod]
−
 
+
* [http://www.mcs.anl.gov/~leyffer/macepec/EPEC-PCa.mod EPEC-PCa.mod]
−
EPEC-GJ.mod runs using solve-GJ.com<br />[EPEC-GS.mod EPEC.GS.mod] runs using solve-GS.com  [EPEC-MPEC.mod <br />EPEC-MPEC.mod]  [EPEC-NCP.mod <br />EPEC-NCP.mod]  [EPEC-NCPa.mod <br />EPEC-NCPa.mod]  [EPEC-NCPt.mod <br />EPEC-NCPt.mod] runs using solve-t.com  [EPEC-NLP.mod <br />EPEC-NLP.mod]  [EPEC-PC.mod <br />EPEC-PC.mod] <br />EPEC-PCa.mod  
 
−
 
 
−
</blockquote>
 
  
 
Sample data files are in three groups (different sizes):
 
Sample data files are in three groups (different sizes):
 +
# Size 1: 2 leaders with 8 variables and 4 constraints; 16 follower variables
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0001.dat rand-0001.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0002.dat rand-0002.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0003.dat rand-0003.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0004.dat rand-0004.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0005.dat rand-0005.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0006.dat rand-0006.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0007.dat rand-0007.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0008.dat rand-0008.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0009.dat rand-0009.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0010.dat rand-0010.dat]
 +
# Size 2: 2 leaders with 16 variables and 8 constraints; 32 follower variables
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0011.dat rand-0011.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0012.dat rand-0012.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0013.dat rand-0013.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0014.dat rand-0014.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0015.dat rand-0015.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0016.dat rand-0016.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0017.dat rand-0017.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0018.dat rand-0018.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0019.dat rand-0019.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0020.dat rand-0020.dat]
 +
# Size 3: 4 leaders with 16 variables and 8 constraints; 32 follower variables
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0021.dat rand-0021.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0022.dat rand-0022.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0023.dat rand-0023.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0024.dat rand-0024.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0025.dat rand-0025.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0026.dat rand-0026.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0027.dat rand-0027.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0028.dat rand-0028.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0029.dat rand-0029.dat]
 +
## [http://www.mcs.anl.gov/~leyffer/macepec/rand-0030.dat rand-0030.dat]
  
−
<blockquote>
+
==== ex-001 ====
−
 
+
A small EPEC for which with a price-consistent formulations exists:
−
Size 1: rand-0001.dat rand-0002.dat rand-0003.dat rand-0004.dat rand-0005.dat rand-0006.dat rand-0007.dat rand-0008.dat rand-0009.dat rand-0010.dat<br /> Size 2: rand-0011.dat rand-0012.dat rand-0013.dat rand-0014.dat rand-0015.dat rand-0016.dat rand-0017.dat rand-0018.dat rand-0019.dat rand-0020.dat<br /> Size 2: rand-0021.dat rand-0022.dat rand-0023.dat rand-0024.dat rand-0025.dat rand-0026.dat rand-0027.dat rand-0028.dat rand-0029.dat rand-0030.dat
+
* [http://www.mcs.anl.gov/~leyffer/macepec/ex-001-GJ.mod ex-001-GJ.mod]
−
 
+
* [http://www.mcs.anl.gov/~leyffer/macepec/ex-001-GS.mod ex-001.GS.mod]
−
</blockquote>
+
* [http://www.mcs.anl.gov/~leyffer/macepec/ex-001-MPEC.mod ex-001-MPEC.mod]  
−
----
+
* [http://www.mcs.anl.gov/~leyffer/macepec/ex-001-NCP.mod ex-001-NCP.mod]  
−
 
+
* [http://www.mcs.anl.gov/~leyffer/macepec/ex-001-NCPa.mod ex-001-NCPa.mod]
−
ex-001 small EPEC for which with a price-consistent formulations exists:
+
* [http://www.mcs.anl.gov/~leyffer/macepec/ex-001-NCPt.mod ex-001-NCPt.mod]
−
 
+
* [http://www.mcs.anl.gov/~leyffer/macepec/ex-001-NLP.mod ex-001-NLP.mod]
−
<blockquote>
+
* [http://www.mcs.anl.gov/~leyffer/macepec/ex-001-PC.mod ex-001-PC.mod]
−
 
+
* [http://www.mcs.anl.gov/~leyffer/macepec/ex-001-PCa.mod ex-001-PCa.mod]
−
[ex-001-GJ.mod ex-001-GJ.mod<br />][ex-001-GS.mod ex-001.GS.mod]Â [ex-001-MPEC.mod <br /> ex-001-MPEC.mod]Â [ex-001-NCP.mod <br /> ex-001-NCP.mod]Â [ex-001-NCPa.mod <br /> ex-001-NCPa.mod]Â [ex-001-NCPt.mod <br /> ex-001-NCPt.mod]Â [ex-001-NLP.mod <br /> ex-001-NLP.mod]Â [ex-001-PC.mod <br /> ex-001-PC.mod]Â <br />ex-001-PCa.mod
 
−
 
 
−
</blockquote>
 
−
----
 
−
 
 
−
ex-4 small EPEC from Fukushima and Pang which does not have a solution.
 
−
 
 
−
<blockquote>
 
−
 
 
−
[ex-4-GJ.mod ex-4-GJ.mod<br />][ex-4-GS.mod ex-4.GS.mod]Â [ex-4-MPEC.mod <br /> ex-4-MPEC.mod]Â [ex-4-NCP.mod <br /> ex-4-NCP.mod]Â [ex-4-NCPa.mod <br /> ex-4-NCPa.mod]Â [ex-4-NCPt.mod <br /> ex-4-NCPt.mod]Â [ex-4-NLP.mod <br /> ex-4-NLP.mod]Â [ex-4-PC.mod <br /> ex-4-PC.mod]Â <br />ex-4-PCa.mod
 
−
 
 
−
</blockquote>
 
−
----
 
−
 
 
−
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.
 
−
 
 
−
<blockquote>
 
−
 
 
−
[outrata3-GJ.mod outrata3-GJ.mod<br />][outrata3-GS.mod outrata3.GS.mod]Â [outrata3-MPEC.mod <br /> outrata3-MPEC.mod]Â [outrata3-NCP.mod <br /> outrata3-NCP.mod]Â [outrata3-NCPa.mod <br /> outrata3-NCPa.mod]Â [outrata3-NCPt.mod <br /> outrata3-NCPt.mod]Â [outrata3-NLP.mod <br /> outrata3-NLP.mod]Â [outrata3-PC.mod <br /> outrata3-PC.mod]Â <br />outrata3-PCa.mod
 
−
 
 
−
</blockquote>
 
−
----
 
  
−
outrata4  is derived from outrata3 so that a price-consistent solution to this model exists.  
+
==== ex-4 ====
 +
A small EPEC from Fukushima and Pang which does not have a solution.
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/ex-4-GJ.mod ex-4-GJ.mod]
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/ex-4-GS.mod ex-4.GS.mod]
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/ex-4-MPEC.mod ex-4-MPEC.mod]
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/ex-4-NCP.mod ex-4-NCP.mod]
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/ex-4-NCPa.mod ex-4-NCPa.mod]
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/ex-4-NCPt.mod ex-4-NCPt.mod]
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/ex-4-NLP.mod ex-4-NLP.mod]
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/ex-4-PC.mod ex-4-PC.mod]
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/ex-4-PCa.mod ex-4-PCa.mod]
  
−
<blockquote>
+
==== 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.
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/outrata3-GJ.mod outrata3-GJ.mod]
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/outrata3-GS.mod outrata3.GS.mod]
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/outrata3-MPEC.mod outrata3-MPEC.mod]
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/outrata3-NCP.mod outrata3-NCP.mod]
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/outrata3-NCPa.mod outrata3-NCPa.mod]
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/outrata3-NCPt.mod outrata3-NCPt.mod]
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/outrata3-NLP.mod outrata3-NLP.mod]
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/outrata3-PC.mod outrata3-PC.mod]
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/outrata3-PCa.mod outrata3-PCa.mod]
  
−
[outrata4-GJ.mod outrata4-GJ.mod<br />][outrata4-GS.mod outrata4.GS.mod] [outrata4-MPEC.mod <br /> outrata4-MPEC.mod]Â [outrata4-NCP.mod <br /> outrata4-NCP.mod]Â [outrata4-NCPa.mod <br /> outrata4-NCPa.mod]Â [outrata4-NCPt.mod <br /> outrata4-NCPt.mod]Â [outrata4-NLP.mod <br /> outrata4-NLP.mod]Â [outrata4-PC.mod <br /> outrata4-PC.mod]Â <br />outrata4-PCa.mod
+
==== outrata4 ====
 +
This EPEC  is derived from outrata3 so that a price-consistent solution to this model exists.
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/outrata4-GJ.mod outrata4-GJ.mod]
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/outrata4-GS.mod outrata4.GS.mod]  
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/outrata4-MPEC.mod outrata4-MPEC.mod]
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/outrata4-NCP.mod outrata4-NCP.mod]
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/outrata4-NCPa.mod outrata4-NCPa.mod]
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/outrata4-NCPt.mod outrata4-NCPt.mod]
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/outrata4-NLP.mod outrata4-NLP.mod]
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/outrata4-PC.mod outrata4-PC.mod]
 +
* [http://www.mcs.anl.gov/~leyffer/macepec/outrata4-PCa.mod outrata4-PCa.mod]
  
−
</blockquote>
+
__NOTOC__

Latest revision as of 16:16, 5 March 2009

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:

  1. 2006-04-27: corrected mistake in outrata4-GS/outrata4-GJ objective definition (now 10*y[4]^2)
  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.

There are three data files for different networks:

  1. electric-001.dat a small 3 node infeasible problem
  2. electric-002.dat a small 3 node feasible problem
  3. electric-003.dat derived from an 18 node real example of the PJM market from the eastern United States
  4. 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 *

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

  1. Size 1: 2 leaders with 8 variables and 4 constraints; 16 follower variables
    1. rand-0001.dat
    2. rand-0002.dat
    3. rand-0003.dat
    4. rand-0004.dat
    5. rand-0005.dat
    6. rand-0006.dat
    7. rand-0007.dat
    8. rand-0008.dat
    9. rand-0009.dat
    10. rand-0010.dat
  2. Size 2: 2 leaders with 16 variables and 8 constraints; 32 follower variables
    1. rand-0011.dat
    2. rand-0012.dat
    3. rand-0013.dat
    4. rand-0014.dat
    5. rand-0015.dat
    6. rand-0016.dat
    7. rand-0017.dat
    8. rand-0018.dat
    9. rand-0019.dat
    10. rand-0020.dat
  3. Size 3: 4 leaders with 16 variables and 8 constraints; 32 follower variables
    1. rand-0021.dat
    2. rand-0022.dat
    3. rand-0023.dat
    4. rand-0024.dat
    5. rand-0025.dat
    6. rand-0026.dat
    7. rand-0027.dat
    8. rand-0028.dat
    9. rand-0029.dat
    10. rand-0030.dat

ex-001

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

ex-4

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

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.

outrata4

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


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