GAMS — The Solver Manuals - Available Software

528 SNOPT
* fill with random data
x(i) = uniform(1,10);
y(i) = uniform(1,10);
variables
a
b
r
equations
e(i)
x coordinate of center of circle
y coordinate of center of circle
radius;
points must be inside circle;
e(i).. sqr(x(i)-a) + sqr(y(i)-b) =l= sqr(r);
r.lo = 0;
model m /all/;
option nlp=snopt;
solve m using nlp minimizing r;
Without help, SNOPT will not be able to find an optimal solution. The problem will be declared infeasible. In
this case, providing a good starting point is very easy. If we define
then good estimates are
Thus we include in our model:
x min = min
i
x i ,
y min = min
i
y i ,
x max = max
i
y max = max
i
a = (x min + x max )/2,
b = (y min + y max )/2,
x i ,
y i ,
r = √ (a − x min ) 2 + (b − y min ) 2 .
parameters xmin,ymin,xmax,ymax;
xmin = smin(i, x(i));
ymin = smin(i, x(i));
xmax = smax(i, x(i));
ymax = smax(i, y(i));
* set starting point
a.l = (xmin+xmax)/2;
b.l = (ymin+ymax)/2;
r.l = sqrt( sqr(a.l-xmin) + sqr(b.l-ymin) );
and now the model solves very easily.
Level values can also be set implicitly as a result of assigning bounds. When a variable is bounded away from
zero, for instance by the statement Y.LO = 1;, the SOLVE statement will override the default level of zero of such
a variable in order to make it feasible.
Note: another way to formulate the model would be to minimize r 2 instead of r. This allows SNOPT to solve
the problem even with the default starting point.