* System of nonlinear equations
* Robot kinematics problem (Kearfott and Novoa, 1990).
* 16 known solutions

* Sets
SET i /1*8/;

VARIABLES
	 x(i)  
	 s  
     objval    objective function variable;

FREE VARIABLES    objval;


EQUATIONS
	 f Objective function
	 h1p
	 h1m
	 h2p
	 h2m
	 h3p
	 h3m
	 h4  
	 h5p  
	 h5m  
	 h6p  
	 h6m  
	 h7p  
	 h7m  
	 h8p  
	 h8m  ;

f  .. objval =e=s;
h1p  .. -s-0.1238*x('1') + x('7') - 0.001637*x('2') - 0.9338*x('4') + 0.004731*x('1')*x('3') - 0.3578*x('2')*x('3') =l= 0.3571;
h1m  .. -s+0.1238*x('1') - x('7') + 0.001637*x('2') + 0.9338*x('4') - 0.004731*x('1')*x('3') + 0.3578*x('2')*x('3') =l= -0.3571;
h2p  .. -s+0.2638*x('1') - x('7') - 0.07745*x('2') - 0.6734*x('4') + 0.2238*x('1')*x('3') + 0.7623*x('2')*x('3') =l= 0.6022;
h2m  .. -s-0.2638*x('1') + x('7') + 0.07745*x('2') + 0.6734*x('4') - 0.2238*x('1')*x('3') - 0.7623*x('2')*x('3') =l= -0.6022;
h3p  .. -s+0.3578*x('1') + 0.004731*x('2') + x('6')*x('8') =l= 0;
h3m  .. -s-0.3578*x('1') - 0.004731*x('2') - x('6')*x('8') =l= 0;
h4  .. -0.7623*x('1') + 0.2238*x('2') =e= -0.3461;
h5p  .. -s + POWER(x('1'),2) + POWER(x('2'),2) =l= 1;
h5m  .. -s -POWER(x('1'),2) -POWER(x('2'),2) =l= -1;
h6p  .. -s + POWER(x('3'),2) + POWER(x('4'),2) =l= 1;
h6m  .. -s -POWER(x('3'),2) -POWER(x('4'),2) =l= -1;
h7p  .. -s + POWER(x('5'),2) + POWER(x('6'),2) =l= 1;
h7m  .. -s -POWER(x('5'),2) -POWER(x('6'),2) =l= -1;
h8p  .. -s + POWER(x('7'),2) + POWER(x('8'),2) =l= 1;
h8m  .. -s -POWER(x('7'),2) -POWER(x('8'),2) =l= -1;

* Bounds
x.LO(i)  = -1;
x.UP(i)  = 1;

* Starting point
* x.L('1') = 0.1644;
* x.L('2') = -0.9864;
* x.L('3') = -0.9471;
* x.L('4') = -0.3210;
* x.L('5') = -0.9982;
* x.L('6') = -0.0594;
* x.L('7') = 0.4110;
* x.L('8') = 0.9116;

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