// Problem K1 (indefinite QP)

OPTIONS{
brstra: 1;   // use bisection as the branching strategy
} 

// The interface to the IQP module is not available in this distribution.
// Instead of the IQP module, we will use the general-purpose factorable 
// NLP module to solve the problem.

MODULE: NLP;

POSITIVE_VARIABLES x1, x2, x3, x4;

EQUATIONS e1, e2, e3, e4, e5, e6;

e1: x1+4*x2 <= 8;

e2: 4*x1+x2 <= 12;

e3: 3*x1+4*x2 <= 12;

e4: 2*x3+x4 <= 8;

e5: x3+2*x4 <= 8;

e6: x3+x4 <= 5;


OBJ: minimize x1 - x2 - x3 - x1*x3 + x1*x4 + x2*x3 - x2*x4;