$title Cone Equation Errors (cerr1,SEQ=495)
$onText

This model checks if Cmex creates an error as expected when dealing with cone
equations. The errors we want to get are:
- RHS for =C= has to be 0.0
- =C= equations cannot be scaled
- Variables with =C= entries have to be continous
- Variable enters more than one =C= equation

Contributor: Lutz Westermann

$offText

$onEcho > err.gms
set n / n1*n4 /;
parameter d(n), l(n), u(n);

d(n) = uniform(1,2);
l(n) = uniform(0.1,10);
u(n) = l(n) + uniform(0,12-l(n));

Variables x(n);
x.l(n) = uniform(l(n), u(n));

x.lo(n) = l(n);
x.up(n) = u(n);

Variables t(n), z(n), obj;
Equations defobjc, cone(n);

defobjc..     sum(n, d(n)*t(n)) =e= obj;
cone(n)..     x(n) + t(n) =c= z(n) + 1;

model clp  /all/;
solve clp  min obj using lp;
$offEcho

$call =gams err.gms lo=%GAMS.lo% lp=mosek
$if not errorlevel 1 $abort should get error because of RHS <> 0

$onEcho > err.gms
set n / n1*n4 /;
parameter d(n), l(n), u(n);

d(n) = uniform(1,2);
l(n) = uniform(0.1,10);
u(n) = l(n) + uniform(0,12-l(n));

Variables x(n);
x.l(n) = uniform(l(n), u(n));

x.lo(n) = l(n);
x.up(n) = u(n);

Variables t(n), z(n), obj;
Equations defobjc, cone(n);

defobjc..     sum(n, d(n)*t(n)) =e= obj;
cone(n)..     x(n) + t(n) =c= z(n);

model clp  /all/;
cone.scale(n) = 2;
solve clp  min obj using lp;
$offEcho

$call =gams err.gms lo=%GAMS.lo% lp=mosek
$if not errorlevel 1 $abort should get error because of scaling

$onEcho > err.gms
set n / n1*n4 /;
parameter d(n), l(n), u(n);

d(n) = uniform(1,2);
l(n) = uniform(0.1,10);
u(n) = l(n) + uniform(0,12-l(n));

Variables x(n);
x.l(n) = uniform(l(n), u(n));

x.lo(n) = l(n);
x.up(n) = u(n);

Variables t(n), z(n), obj;
Integer Variables t;
Equations defobjc, cone(n);

defobjc..     sum(n, d(n)*t(n)) =e= obj;
cone(n)..     x(n) + t(n) =c= z(n);

model clp  /all/;
solve clp  min obj using mip;
$offEcho

$call =gams err.gms lo=%GAMS.lo% mip=mosek
$if not errorlevel 1 $abort should get error because of integer variables

$onEcho > err.gms
set n / n1*n4 /;
parameter d(n), l(n), u(n);

d(n) = uniform(1,2);
l(n) = uniform(0.1,10);
u(n) = l(n) + uniform(0,12-l(n));

Variables x(n);
x.l(n) = uniform(l(n), u(n));

x.lo(n) = l(n);
x.up(n) = u(n);

Variables t(n), z(n), obj;
Equations defobjc, cone(n), cone2(n);

defobjc ..     sum(n, d(n)*t(n)) =e= obj;
cone(n) ..     x(n) + t(n) =c= z(n);
cone2(n)..     x(n) + t(n) =c= z(n);

model clp  /all/;
solve clp  min obj using lp;
$offEcho

$call =gams err.gms lo=%GAMS.lo% lp=mosek
$if not errorlevel 1 $abort should get error because of variables in more than one =c= equation