$TITLE Test Problem

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Tapio Westerlund & Joakim Westerlund
GGPECP -- An algorithm for solving non-convex MINLP problems by
cutting plane and transformation techniques
Proceedings of ICHEAP-6, Pisa, June 2003.

# define the objective function based on continuous variable x
    # and discrete (integer) variable y.
    f "3*y-5*x"
    # define the inequality contraints. this is a set of equations
    # where the last expression should evaluate to a vector of
    # values. A feasible point is one for which all the values in this
    # vector are non-positive.
    g 
	c1 = 2*y + 3*x - 24
	c2 = 3*x - 2*y - 8
	c3 = 2*y^2 - 2*sqrt(y) + 11*y + 8*x - 39 - 2*sqrt(x)*y^2
	{c1, c2, c3}
    end
    # specify the lower bounds on both the continuous and integer
    # optimization variables. Two vectors are expected, the first for
    # the continuous (real) variables and the second for the integer
    # variables.
    a 1 1
    # and also specify the upper bounds on these variables
    b 6 6
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* Example from Problem 8.26 in "Engineering Optimization" 
* by Reklaitis, Ravindran and Ragsdell (1983) 
* Code from http://www.che.boun.edu.tr/courses/che477/gms-mod.html#TEST.GMS
* (course by Ignacio Grossmann)

VARIABLES x, y, z ; 
POSITIVE VARIABLES x;
integer variables y;

EQUATIONS con1, con2, con3, obj;

con1.. 2*y+3*x =l= 24;
con2.. 3*x - 2*y =l= 8;
con3.. 2*y*y - 2*sqrt(y) + 11*y + 8*x =l= 39 + 2*sqrt(x)*y*y;
obj..  z =e= 3*y - 5*x;

* Upper bounds 
  x.up = 6;
  y.up = 6;
* lower bounds
  x.lo = 1;
  y.lo = 1;

model westerlund /all/;