I think I must be misinterpreting your suggestion. I have tried several variations of what I think it means, but nothing seems to work.
Did you mean to take the square root of the variables in the original objective function without transforming the variables in the constraints? So because X1 = Y1^2, etc, then Obj = aX1^0.5 + ... = aY1 + ... subject to: X1 + ... =< b.
Everything I have tried either stopped because a negative number was passed into the square root, or has made the problem less stable. Am I completely missing the point?
"John D'Errico" <email@example.com> wrote in message <firstname.lastname@example.org>... > "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. > > John