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. 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 > >______________________________________________ >[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. > > > > ______________________________________________ [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.
