On 5/10/07, Spencer Graves <[EMAIL PROTECTED]> wrote: > > I don't know of any sources, but the idea is quite simple. > > > > For each constraint that is broken, the penalty is the amount > > by which the constraint is broken times a penalty rate. The > > total penalty to add to the objective is the sum of penalties > > over all constraints. > > > > There is a catch or two when using this with derivative-based > > optimizers. The objective typically becomes non-differentiable > > at the boundary, and optimizers can get confused. > I believe I've gotten good results with penalties that are the SQUARE of > the amount by which the constraints were violated. These are > continuously differentiable and so don't confuse the derivative-based > optimizers much. > > Also, I start with a small penalty, then increase the penalty until I > get a solution that seems sensible. If you can't handle a solution just > a little outside your constraints, shrink a little the place at which > the penalty starts. > > Hope this helps. > Spencer Graves > > > They might > > be less confused with smaller penalty rates. However if the > > penalty rate is too small, then you can get a "solution" that breaks > > one or more penalties. > > > > Starting from a solution given by Rgenoud or its ilk is probably > > a good idea. > > > > Patrick Burns > > [EMAIL PROTECTED] > > +44 (0)20 8525 0696 > > http://www.burns-stat.com > > (home of S Poetry and "A Guide for the Unwilling S User") > > > > Paul Smith wrote: > > > > > >> Dear All > >> > >> I am dealing at the moment with optimization problems with nonlinear > >> constraints. Regenoud is quite apt to solve that kind of problems, but > >> the precision of the optimal values for the parameters is sometimes > >> far from what I need. Optim seems to be more precise, but it can only > >> accept box-constrained optimization problems. I read in the list > >> archives that optim can also be used with nonlinear constrains through > >> penalizations. However, I am not familiar with the technique of > >> penalizations. Could someone please indicate to me a site or a book to > >> learn about that penalization technique? > >> > >> Thanks in advance,
Thanks to all. I have meanwhile had a look at Fletcher's book (as suggested by Ravi) and I think that now I understand the idea behind using penalties with constrained optimization problems. Paul ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
