* NLP literature problem
* Murtagh and Saunders (19993)

VARIABLES
	 x1  
	 x2  
	 x3  
	 x4  
	 x5  
     objval    objective function variable;

FREE VARIABLES    objval;


EQUATIONS
	 g1  
	 g2  
	 g3  
	 g4  
	 g5  
	 f Objective function;

f  .. objval =e=POWER(x1-1,2)+POWER(x1-x2,2)+POWER(x2-x3,3)+POWER(x3-x4,4)+POWER(x4-x5,4);
g1  .. x1+POWER(x2,2)+POWER(x3,3) =l= 2+3*SQRT(2);
g2  .. -x1-POWER(x3,3)-POWER(x2,2) =l= -2-3*SQRT(2);
g3  .. x2+x4-POWER(x3,2) =l= -2+2*SQRT(2);
g4  .. -x2-x4+POWER(x3,2) =l= 2-2*SQRT(2);
g5  .. 0.5*x1*x5+0.5*x1*x5 =e= 2;

* Bounds
x1.LO = -5; x1.UP = 5;
x2.LO = -5; x2.UP = 5;
x3.LO = -5; x3.UP = 5;
x4.LO = -5; x4.UP = 5;
x5.LO = -5; x5.UP = 5;

* Starting point (global solution)
* x1.L = 1.1166;
* x2.L = 1.2204;
* x3.L = 1.5378;
* x4.L = 1.9728;
* x5.L = 1.7911;

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