"Mike " <michael.gerstREMOVE@yale.edu> wrote in message <email@example.com>... > Bruno and John, thanks for the tip. > > If I understand you correctly, the following simple LP problem > > Obj = a*X1 + a*X2 + a*X3 > subject to: X1 + X2 + X3 =< b > > would transform to > > Obj = a*sqrt(X1^2) + b*sqrt(X2^2) + c*sqrt(X3^2) > subject to: sqrt(X1^2) + sqrt(X2^2) + sqrt(X3^2) =< b > > Is this the basic idea?
Not exactly. Have the optimizer vary a vecotr with three unknowns in it [Y1,Y2,Y3]. Inside the objective function, transform your variables so that
X1 = Y1^2 X2 = Y2^2 X3 = Y3^2
So now X1, X2, X3 are assured to be positive.
When the optimization is done, and it returns the vector [Y1, Y2, Y3], just square the elements to recover [X1, X2, X3].
There are similar strategies to deal with variables that have both upper and lower bounds.