! Find minimum circle radius that encloses             (CircleMin.lng)
 a set of points in 2-space;
! Keywords: Circle, Circumscribe, Cone, Enclosing circle, Euclidean distance, 
    Hull, LINGO, Radius, Second order cone, SOC;
SETS:
 POINT: x, y;
ENDSETS
DATA:
 ! These happen to be corner points of a maximum area polygon for which 
the distance between any pair is <= 1;
  x = 0.4514926  0.2357990  -0.1126499 -0.4473675  -0.5421421  0.000000;
  y = 0.4561146  0.9718018   0.9936347  0.8943502   0.3434647  0.000000;
ENDDATA

! Variables:
    x0 = x coordinate of the center of enclosing circle,
    y0 = y coordinate of the center of enclosing circle
     R = radius of circle;
! Minimize the radius;
MIN = R;

@FREE( x0); @FREE( y0);
! Each point must be distance <= r from center of circle,
 using Euclidean distance.
 This happens to be a second order cone constraint;
@FOR( POINT(i):
   ( x(i) - x0)^2 + ( y(i) - y0)^2 <= r^2;
    );