* System of nonlinear equations
* Ferraris and Tronconi (1986)
* 2 known solutions

* Parameters
SCALAR pi  /3.1415927 /;

SCALAR e  /2.7182818 /;

VARIABLES
	 x1  
	 x2  
	 s  
     objval    objective function variable;

FREE VARIABLES    objval;


EQUATIONS
	 h1p  
	 h2p  
	 h1m  
	 f Objective function
	 h2m  ;

f  .. objval =e=s;
h1p  .. -0.25/pi*x2 - 0.5*x1 - s + 0.5*SIN(x1*x2) =l= 0;
h1m  .. 0.25/pi*x2 + 0.5*x1 - s  -0.5*SIN(x1*x2) =l= 0;
h2p  .. e/pi*x2 - 2*e*x1 - s + (1 - 0.25/pi)*(EXP(2*x1) - e) =l= 0;
h2m  .. -e/pi*x2 - s  -(1 - 0.25/pi)*(EXP(2*x1) - e) + 2*e*x1 =l= 0;

* Bounds
x1.LO = 0.25;
x1.UP = 1;
x2.LO = 1.5;
x2.UP = 6.28;

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