cns02.gms : Test how bounds change a 2-variable CNS model
This is a simple two by two CNS model solved with varying bounds.
Small Model of Type: CNS
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$title Test how bounds change a 2-variable CNS model (cns02,SEQ=92)
$ontext
This is a simple two by two CNS model solved with varying bounds.
$offtext
maxexecerror = 1;
$if not set TESTTOL $set TESTTOL 1e-6
scalar tol / %TESTTOL% /;
variable x, y;
equation f, g;
model cns02 / f, g /;
f .. x*x + .001*y =e= 4;
g .. x + y =e= 8;
option limrow = 0, limcol = 0, decimals=8;
scalar x1, y1, x2, y2, det;
* 1000*f - g yields 1000x^2 - x - 3992 = 0
det = sqrt(1 + 4 * 1000 * 3992);
x1 = (1 + det)/ 2000;
x2 = (1 - det)/ 2000;
y1 = 8 - x1;
y2 = 8 - x2;
display x1, x2, y1, y2;
* Case 1: No bounds on the variables. The model should solve fine.
x.lo = -INF; x.up = INF; x.l = 8; solve cns02 using cns;
abort$(cns02.solvestat <> 1 or cns02.modelstat <> 16) 'bad return codes';
abort$((abs(x.l-x1) <= tol and abs(y.l-y1) <= tol)
eqv (abs(x.l-x2) <= tol and abs(y.l-y2) <= tol)) 'x or y is wrong',x.l,y.l;
* Case 2: No bounds on the variables. The model should again solve
* fine, but the solution can be different because the initial
* value of x is different.
x.lo = -INF; x.up = INF; x.l = -8; solve cns02 using cns;
abort$(cns02.solvestat <> 1 or cns02.modelstat <> 16) 'bad return codes';
abort$((abs(x.l-x1) <= tol and abs(y.l-y1) <= tol)
eqv (abs(x.l-x2) <= tol and abs(y.l-y2) <= tol)) 'x or y is wrong',x.l,y.l;
* Case 3: The bound on x will make solution unique (feasible).
x.lo = 1; x.up = 3; x.l = 8; solve cns02 using cns;
abort$(cns02.solvestat <> 1 or cns02.modelstat <> 16) 'bad return codes';
abort$(abs(x.l-x1) > tol or abs(y.l-y1) > tol) 'x or y is wrong',x.l,y.l;
* Case 4: The bound on x will make the model infeasible.
x.lo = 2; x.up = 3; x.l = 8; solve cns02 using cns;
abort$(cns02.solvestat <> 1 or cns02.modelstat <> 5) 'bad return codes';
abort$(cns02.numinfes < 1) 'wrong .numinfes';
* Case 5 and 6: X is fixed and the model is not square any more.
cns02.holdfixed = 0; x.lo = 2; x.up = 2; x.l = 8; solve cns02 using cns;
abort$(execerror=0) 'previous solve should have given exec errors';
abort$(cns02.solvestat <> 12 or cns02.modelstat <> 14) 'bad return codes';
execerror = 0;
cns02.holdfixed = 1; x.lo = 2; x.up = 2; x.l = 8; solve cns02 using cns;
abort$(execerror=0) 'previous solve should have given exec errors';
abort$(cns02.solvestat <> 12 or cns02.modelstat <> 14) 'bad return codes';
execerror = 0;
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