* Generalized geometric programming problem
* Manousouthiakis and Sourlas (1992)

* Parameters
SCALAR k1   / 0.09755988 /;

SCALAR k2   / 0.99 /;

SCALAR k3   / 0.0391908 /;

SCALAR k4   / 0.9 /;

VARIABLES
	 x1  
	 x2  
	 x3  
	 x4  
	 x5  
	 x6  
     objval    objective function variable;

FREE VARIABLES    objval;


EQUATIONS
	 f Objective function
	 g1  
	 g2  
	 g3  
	 g4  
	 g5  ;

f  .. objval =e= -x4;
g1  .. x1 + k1 * x1 * x5 =e= 1;
g2  .. x2 - x1 + k2*k1 * x2 * x6 =e= 0;
g3  .. x3 + x1 + k3 * x3 * x5 =e= 1;
g4  .. x4 - x3 + x2 - x1 + k4 * k3 * x4 * x6 =e= 0;
g5  .. x5**0.5 + x6**0.5 =l= 4;

* Bounds
x1.LO = 0; x1.UP = 1;
x2.LO = 0; x2.UP = 1;
x3.LO = 0; x3.UP = 1;
x4.LO = 0; x4.UP = 1;
x5.LO = 1e-05; x5.UP = 16;
x6.LO = 1e-05; x6.UP = 16;

* Starting point (global solution)
* x1.L = 0.772; x2.L = 0.517; x3.L = 0.204; 
* x4.L = 0.388; x5.L = 3.036; x6.L = 5.097;

MODEL test /ALL/;
SOLVE test USING NLP MINIMIZING objval;