cns07.gms : CNS model with globally unique solution
The following model has a globally unique solution even though it
is nonlinear and simultaneous.
Not all solvers will recognize that the solution is globally unique
(hardly any will).
The Jacobian of the model
exp(x1) +1
-1 exp(x2)
has the determinant exp(x1)*exp(x2)+1 and is therefore always strictly
positive (bounded away from zero) and if a solution exist it is
therefore unique.
Small Model of Type: CNS
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$title CNS model with globally unique solution (cns07,SEQ=97)
$ontext
The following model has a globally unique solution even though it
is nonlinear and simultaneous.
Not all solvers will recognize that the solution is globally unique
(hardly any will).
The Jacobian of the model
exp(x1) +1
-1 exp(x2)
has the determinant exp(x1)*exp(x2)+1 and is therefore always strictly
positive (bounded away from zero) and if a solution exist it is
therefore unique.
$offtext
$if not set TESTTOL $set TESTTOL 1e-6
scalar tol / %TESTTOL% /;
scalars rhs1, rhs2;
rhs1 = exp(-1) + (-1);
rhs2 = -(-1) + exp(-1);
variable x1, x2;
equation e1, e2;
e1 .. exp(x1) + x2 =e= rhs1;
e2 .. -x1 + exp(x2) =e= rhs2;
model cns07 / all /;
option limrow = 0, limcol = 0;
solve cns07 using cns;
abort$(cns07.solvestat <> %solvestat.NormalCompletion%
or (cns07.modelstat <> %modelstat.SolvedUnique%) and (cns07.modelstat <> %modelstat.Solved%)) 'bad return codes';
abort$(abs(x1.l+1) > tol) 'bad x1.l';
abort$(abs(x2.l+1) > tol) 'bad x2.l';
abort$(abs(e1.l-rhs1) > tol) 'bad e1.l';
abort$(abs(e2.l-rhs2) > tol) 'bad e2.l';
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