Description

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 e1 can be solved uniquely w.r.t. x1.
Equation e2 can then be solved uniquely w.r.t. x2 even though it
  is nonlinear in x1 since x1 has a unique value.
Equation e3 and e4 are now linear and they can be solved uniquely
  given the values of x1 and x;

Small Model of Type : CNS

Category : GAMS Test library

Main file : cns04.gms

$title CNS model with globally unique solution (cns04,SEQ=94)

$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 e1 can be solved uniquely w.r.t. x1.
  Equation e2 can then be solved uniquely w.r.t. x2 even though it
    is nonlinear in x1 since x1 has a unique value.
  Equation e3 and e4 are now linear and they can be solved uniquely
    given the values of x1 and x;
$offtext

$if not set TESTTOL $set TESTTOL 1e-6
scalar tol / %TESTTOL% /;

variable x1, x2, x3, x4;
equation e1, e2, e3, e4;

e1 .. x1 =e= 4;
e2 .. x2 =e= sqr(x1);
e3 .. x3 + x4 =e= x1;
e4 .. x3 - x4 =e= x2;

model cns04 / all /;
option limrow = 0, limcol = 0;
solve cns04 using cns;
abort$(cns04.solvestat <> %solvestat.NormalCompletion%
   or (cns04.modelstat <> %modelstat.SolvedUnique%) and (cns04.modelstat <> %modelstat.Solved%))  'bad return codes';
abort$(abs(x1.l- 4) > tol)       'bad x1.l';
abort$(abs(x2.l-16) > tol)       'bad x2.l';
abort$(abs(x3.l-10) > tol)       'bad x3.l';
abort$(abs(x4.l+ 6) > tol)       'bad x4.l';
abort$(abs(e1.l- 4) > tol)       'bad e1.l';
abort$(abs(e2.l- 0) > tol)       'bad e2.l';
abort$(abs(e3.l- 0) > tol)       'bad e3.l';
abort$(abs(e4.l- 0) > tol)       'bad e4.l';