* Generalized geometric programming problem
* Heat exchanger network design, Avriel and Williams (1971).

VARIABLES
	 x1  
	 x2  
	 x3  
	 x4  
	 x5  
	 x6  
	 x7  
	 x8  
     objval    objective function variable;

FREE VARIABLES    objval;


EQUATIONS
	 f Objective function
	 f1  
	 f2  
	 f3  
	 f4  
	 f5  
	 f6  ;

f  .. objval =e=x1 + x2 + x3;
f1  .. 833.33252/x1*x4/x6 + 100/x6 - 83333.333/x1/x6 =l= 1;
f2  .. 1250/x2*x5/x7 + x4/x7 - 1250/x2*x4/x7 =l= 1;
f3  .. 1250000/x3/x8 + x5/x8 - 2500/x3*x5/x8 =l= 1;
f4  .. 0.0025 * x4 + 0.0025 * x6 =l= 1;
f5  .. -0.0025*x4 + 0.0025*x5 + 0.0025*x7 =l= 1;
f6  .. -0.01 * x5 + 0.01 * x8 =l= 1;

* Bounds
x1.LO = 100; x1.UP = 10000;
x2.LO = 1000; x2.UP = 10000;
x3.LO = 1000; x3.UP = 10000;
x4.LO = 10; x4.UP = 1000;
x5.LO = 10; x5.UP = 1000;
x6.LO = 10; x6.UP = 1000;
x7.LO = 10; x7.UP = 1000;
x8.LO = 10; x8.UP = 1000;

* Starting point (global solution)
* x1.L = 579.307;
* x2.L = 1359.971;
* x3.L = 5109.971;
* x4.L = 182.018;
* x5.L = 295.601;
* x6.L = 217.982;
* x7.L = 286.417;
* x8.L = 395.601;

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