Hi, Patrick, Paul, et al.: <see in line>
Patrick Burns 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, >> >> Paul >> >> ______________________________________________ >> R-help@stat.math.ethz.ch 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. >> >> >> >> >> > > ______________________________________________ > R-help@stat.math.ethz.ch 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. > ______________________________________________ R-help@stat.math.ethz.ch 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.