// use the general purpose NLP module to solve a small pooling problem

MODULE : NLP;

POSITIVE_VARIABLE x1, x2, x3, x4, x5, x6, x7;

LOWER_BOUNDS{
x2 : 3;
x3 : 1;
x4 : 2;
}

UPPER_BOUNDS{
x1 : 10;
x2 : 20;
x3 : 2;
x4 : 4;
x5 : 10;
x6: 201;
x7: 100;
}

EQUATIONS  e1,e2,e3, e4;

e1 : x3^2+x4^2 <= 12;
e2 : 3 <= x1^2-x2^2+x4^2 <= 100;
e3 : 10 <= x1+x2-5*x3+2*x4 <= 20;
e4 : x4 -x6^2 +4*x7^2 <= 0;

OBJ : minimize 6*x1 + 16*x2 -9*x3 - 10*x4;