Circle Enclosing Points

    {  circle.mpl   }

    {  GAMS Model Library, http://www.gams.com/modlib/libhtml/circle.htm  }

    {  Circle Enclosing Points,  NLP,  Size: 3x10  }



TITLE
    Circle;

OPTIONS
    ModelType=Nonlinear
    ParserType=Extended

INDEX
    i := 1..10;

DATA
    X[i]  := UNIFORM(1,10);
    Y[i]  := UNIFORM(1,10);
    XMin  := MIN(X);
    YMin  := MIN(Y);
    XMax  := MAX(X);
    YMax  := MAX(Y);
    AStart := (XMin+XMax)/2;
    BStart := (YMin+YMax)/2;
    RStart := ((AStart-XMin)^2 + (BStart-YMin)^2)^0.5;


VARIABLES
    A INITIAL AStart;
    B INITIAL BStart;
    R INITIAL RStart;

MODEL

    MIN R;


SUBJECT TO

    E[i]:   (X-A)^2 + (Y-B)^2 <= R^2;


BOUNDS
    0 <= R <= 10;
    0 <= A <= 10;
    0 <= B <= 10;


END