Thank you very much, that is exactly what I wanted to know. I will add the gradient.
Do you have any reference about : "the objective function is additive rather than multiplicative, it has better numerical conditioning" ? I am just being curious :) Gustave 2008/3/5, Ravi Varadhan <[EMAIL PROTECTED]>: > > Hi, > > Let me make the following points in response to your questions: > > 1. Your call to optim() with "L-BFGS-B" as the method is correct. Just > make sure that your function "f" is defined as negative log-likelihood, > since optim is by default a minimizer. The other option is to define > log-likelihood as usual, but set control=list(fnscale=-1). > > 2. You can add derivative (or gradient to be more precise) by defining > that > function and then using the "gr" argument in optim. Specifying exact > gradient almost always improves the convergence of the iterative schemes, > especially for ill-conditioned problems (flat region around the local > minima). So, if it is not too much trouble, and you are confident of your > differentiation skills, you should do that. However, in most cases the > approximate finite-difference gradient used by optim() should be good > enough. > > 3. Regardless of whether it is easy to compute the exact gradient or not, > it is generally a bad idea to maximize the likelihood that involves the > product of a large number of very small numbers. It is almost always > better > to maximize the log-likelihood. Since the objective function is additive > rather than multiplicative, it has better numerical conditioning. > > Ravi. > > > > ---------------------------------------------------------------------------- > ------- > > Ravi Varadhan, Ph.D. > > Assistant Professor, The Center on Aging and Health > > Division of Geriatric Medicine and Gerontology > > Johns Hopkins University > > Ph: (410) 502-2619 > > Fax: (410) 614-9625 > > Email: [EMAIL PROTECTED] > > Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html > > > > > ---------------------------------------------------------------------------- > -------- > > > > -----Original Message----- > From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] > On > Behalf Of Gustave Lefou > Sent: Wednesday, March 05, 2008 1:34 PM > To: r-help@r-project.org > Subject: [R] box-constrained > > Hello everybody, > > I have a question about box-constrained optimization. I've done some > research and I found that optim could do that. Are there other ways in R ? > > Is the following correct if I have a function f of two parameters > belonging > for example to [0,1] and [0,Infinity] ? > optim(par=param, fn=f, method="L-BFGS-B", lower=c(0,0), upper=c(1,Inf)) > > My other question is whether it is possible to add the derivatives of my > function (like in nlm) and whether it is better to add them ? > > If there is no need to add the derivatives, then I guess I could wish to > optimize the likelihood directly rather than to optimize the > log-likelihood... Indeed one aspect of the log-likelihood is to make the > derivatives tractable (in iid cases). Do you agree ? > > Thank you ! > Gustave > > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help@r-project.org 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. > [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org 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.
