Description
This is a fairly simple MPEC model with some useful features: a) it has a unique solution b) it contains all types of matches c) it can be run as an MCP as well as an MPEC Contributor: Steve Dirkse, Jan 2004
Small Model of Type : MPEC
Category : GAMS Test library
Main file : mpec01.gms
$TITLE MPEC model to test all types of matches, using =N= (MPEC01,SEQ=104)
$ontext
This is a fairly simple MPEC model with some useful features:
a) it has a unique solution
b) it contains all types of matches
c) it can be run as an MCP as well as an MPEC
Contributor: Steve Dirkse, Jan 2004
$offtext
$if NOT set MTYPE $set MTYPE mpec
$if not set TESTTOL $set TESTTOL 1e-3
scalar tol / %TESTTOL% /;
variables
z 'objective var',
x 'upper-level control variable',
yL0 'state var: lower bounded, at lower bound',
yL1 'state var: lower bounded, basic',
yU1 'state var: upper bounded, basic',
yU2 'state var: upper bounded, at upper bound',
yF1 'state var: free, basic',
yB0 'state var: double bounded, at lower bound',
yB1 'state var: double bounded, basic',
yB2 'state var: double bounded, at upper bound';
x.l = 1;
yL0.lo = 0; yL0.up = inf; yL0.l = 1;
yL1.lo = 0; yL1.up = inf; yL1.l = 1;
yU1.lo = -inf; yU1.up = 2; yU1.l = 1;
yU2.lo = -inf; yU2.up = 2; yU2.l = 1;
yF1.lo = -inf; yF1.up = inf; yF1.l = 1;
yB0.lo = 0; yB0.up = 2; yB0.l = 1;
yB1.lo = 0; yB1.up = 2; yB1.l = 1;
yB2.lo = 0; yB2.up = 2; yB2.l = 1;
equations
obj,
fL0,
fL1,
fU1,
fU2,
fF1,
fB0,
fB1,
fB2;
obj.. z =e= sqr(x-1.0);
fL0.. 3 * yL0 + 1 * yL1 =N= x - 1;
fL1.. 1 * yL0 + 3 * yL1 =N= x + 2;
fU1.. 3 * yU1 + 1 * yU2 =N= x + 4;
fU2.. 1 * yU1 + 3 * yU2 =N= x + 10;
fF1.. yL0 + yL1 + yU1 + yU2 + 10 * yF1 + yB0 + yB1 + yB2 =N= x + 16;
fB0.. 3 * yB0 + 1 * yB1 + 1 * yB2 =N= x;
fB1.. 1 * yB0 + 3 * yB1 + 1 * yB2 =N= x + 4;
fB2.. 1 * yB0 + 1 * yB1 + 3 * yB2 =N= x + 10;
model alltypes /
$ifi '%MTYPE%' == 'mpec' obj,
fL0.yL0, fL1.yL1,
fU1.yU1, fU2.yU2,
fF1.yF1,
fB0.yB0, fB1.yB1, fB2.yB2 /;
* $ontext this is the optimal solution
yL0.l=0;
yL1.l=1;
yU1.l=1;
yU2.l=2;
yF1.l=1;
yB0.l=0;
yB1.l=1;
yB2.l=2;
* $offtext
option limcol=0,limrow=0;
$ifi NOT '%MTYPE%' == 'mpec' x.fx=1;
solve alltypes using %MTYPE%
$ifi '%MTYPE%' == 'mpec' minimizing z;
* For global solvers we do not require NormalCompletion
$if not set global $set global 0
scalar global /%global%/;
if {(alltypes.solvestat = %solvestat.CapabilityProblems%),
abort$[alltypes.modelstat <> %modelstat.NoSolutionReturned%] 'Wrong status codes',
alltypes.solvestat, alltypes.modelstat;
else
abort$[not((alltypes.solvestat = %solvestat.NormalCompletion% or global) and (alltypes.modelstat = %modelstat.Optimal% or
alltypes.modelstat = %modelstat.LocallyOptimal% or alltypes.modelstat = %modelstat.FeasibleSolution%))] 'Wrong status codes', alltypes.solvestat,
alltypes.modelstat;
* check for correct solution
abort$(abs(yL0.l-0) > tol) 'var yL0.l should be 0', yL0.l;
abort$(abs(yL1.l-1) > tol) 'var yL1.l should be 1', yL1.l;
abort$(abs(yU1.l-1) > tol) 'var yU1.l should be 1', yU1.l;
abort$(abs(yU2.l-2) > tol) 'var yU2.l should be 2', yU2.l;
abort$(abs(yF1.l-1) > tol) 'var yF1.l should be 1', yF1.l;
abort$(abs(yB0.l-0) > tol) 'var yB0.l should be 0', yB0.l;
abort$(abs(yB1.l-1) > tol) 'var yB1.l should be 1', yB1.l;
abort$(abs(yB2.l-2) > tol) 'var yB2.l should be 2', yB2.l;
abort$(abs(fL0.l-1) > tol) 'equ fL0.l should be 1', fL0.l;
abort$(abs(fL1.l-0) > tol) 'equ fL1.l should be 0', fL1.l;
abort$(abs(fU1.l-0) > tol) 'equ fU1.l should be 0', fU1.l;
abort$(abs(fU2.l+4) > tol) 'equ fU2.l should be -4', fU2.l;
abort$(abs(fF1.l-0) > tol) 'equ fF1.l should be 0', fF1.l;
abort$(abs(fB0.l-2) > tol) 'equ fB0.l should be 2', fB0.l;
abort$(abs(fB1.l-0) > tol) 'equ fB1.l should be 0', fB1.l;
abort$(abs(fB2.l+4) > tol) 'equ fB2.l should be -4', fB2.l;
$ ifi not '%MTYPE%' == 'mpec' $goto nompec
abort$(abs(x.l-1) > tol) 'var x.l should be 1', x.l;
abort$(abs(z.l-0) > tol) 'var z.l should be 0', z.l;
abort$(abs(obj.l-0) > tol) 'equ obj.l should be 0', obj.l;
$ label nompec
* TODO - add checks for .m values.
};