cns13.gms : CNS model - solvable, globally unique
The following model has a globally unique solution even though it
is nonlinear.
Not all solvers will recognize that the solution is globally unique.
Equation e3 and e4 can be solved uniquely w.r.t. x3 and x4.
Equation e1 and e2 can then be solved uniquely w.r.t. x1 and x2
even though it is nonlinear in x3 and x4 since x3 and x4 have
unique values.
Small Model of Type: CNS
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$title CNS model - solvable, globally unique (cns13,SEQ=103)
$ontext
The following model has a globally unique solution even though it
is nonlinear.
Not all solvers will recognize that the solution is globally unique.
Equation e3 and e4 can be solved uniquely w.r.t. x3 and x4.
Equation e1 and e2 can then be solved uniquely w.r.t. x1 and x2
even though it is nonlinear in x3 and x4 since x3 and x4 have
unique values.
$offtext
$if not set TESTTOL $set TESTTOL 1e-6
scalar tol / %TESTTOL% /;
scalars rhs1, rhs2, rhs3, rhs4;
rhs1 = 1 + 2 + sqr(3) ;
rhs2 = 1 - 2 + sqr(4);
rhs3 = 3 + 4 ;
rhs4 = 3 - 4 ;
variable x1, x2, x3, x4;
equation e1, e2, e3, e4;
e1 .. x1 + x2 + sqr(x3) =e= rhs1;
e2 .. x1 - x2 + sqr(x4) =e= rhs2;
e3 .. x3 + x4 =e= rhs3;
e4 .. x3 - x4 =e= rhs4;
model m / all /;
solve m using cns;
* we will NOT check for only 15 at this time although this is an easy model
abort$(m.solvestat <> 1 or
(m.modelstat = 15 eqv m.modelstat = 16)) 'bad return codes';
abort$(abs(x1.l-1) > tol) 'bad x1.l';
abort$(abs(x2.l-2) > tol) 'bad x2.l';
abort$(abs(x3.l-3) > tol) 'bad x3.l';
abort$(abs(x4.l-4) > tol) 'bad x4.l';
abort$(abs(e1.l-rhs1) > tol) 'bad e1.l';
abort$(abs(e2.l-rhs2) > tol) 'bad e2.l';
abort$(abs(e3.l-rhs3) > tol) 'bad e3.l';
abort$(abs(e4.l-rhs4) > tol) 'bad e4.l';
abort$(m.numinfes <> 0) 'wrong .numinfes';
abort$(m.numdepnd <> 0) 'wrong .numdepnd';
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