GAMS — The Solver Manuals - Available Software

338 MINOS
4 Modeling Issues
Formulating nonlinear models requires that the modeler pays attention to some details that play no role when
dealing with linear models.
4.1 Starting Points
The first issue is specifying a starting point. It is advised to specify a good starting point for as many nonlinear
variables as possible. The GAMS default of zero is often a very poor choice, making this even more important.
As an (artificial) example consider the problem where we want to find the smallest circle that contains a number
of points (x i , y i ):
Example
minimize r
r,a,b
subject to (x i − a) 2 + (y i − b) 2 ≤ r 2 , r ≥ 0.
This problem can be modeled in GAMS as follows.
set i ’points’ /p1*p10/;
parameters
x(i)
y(i)
’x coordinates’,
’y coordinates’;
* 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=minos;
solve m using nlp minimizing r;
Without help, MINOS 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
x min = min
i
x i ,
y min = min
i
y i ,
x max = max
i
y max = max
i
x i ,
y i ,