Thanks to all for clarifications. So I'm off base, but whether waaay off base depends on whether there is a reasonably well defined optimum to converge to. Which begs the question, I suppose: How does one know whether one has converged to such an optimum? This is always an issue, of course, even for a few parameters; but maybe more so with so many.
-- Bert On Fri, Feb 25, 2011 at 3:35 PM, Ravi Varadhan <rvarad...@jhmi.edu> wrote: > I have worked on a 2D image reconstruction problem in PET (positron emission > tomography) using a Poisson model. Here, each pixel intensity is an unknown > parameter. I have solved problems of size 128 x 128 using an accelerated EM > algorithm. Ken Lange has shown that you can achieve term by term separation > using a minorization inequality, and hence the problem simplifies greatly. > > Ravi. > > ------------------------------------------------------- > Ravi Varadhan, Ph.D. > Assistant Professor, > Division of Geriatric Medicine and Gerontology School of Medicine Johns > Hopkins University > > Ph. (410) 502-2619 > email: rvarad...@jhmi.edu > > -----Original Message----- > From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On > Behalf Of Prof. John C Nash > Sent: Friday, February 25, 2011 5:55 PM > To: Bert Gunter > Cc: r-help@r-project.org > Subject: Re: [R] BFGS versus L-BFGS-B > > For functions that have a reasonable structure i.e., 1 or at most a few > optima, it is > certainly a sensible task. Separable functions are certainly nicer (10K 1D > minimizations), > but it is pretty easy to devise functions e.g., generalizations of > Rosenbrock, Chebyquad > and other functions that are high dimension but not separable. > > Admittedly, there are not a lot of real-world examples that are publicly > available. More > would be useful. > > JN > > > On 02/25/2011 05:06 PM, Bert Gunter wrote: >> On Fri, Feb 25, 2011 at 12:00 PM, Brian Tsai <btsa...@gmail.com> wrote: >>> Hi John, >>> >>> Thanks so much for the informative reply! I'm currently trying to > optimize >>> ~10,000 parameters simultaneously - for some reason, >> >> -- Some expert (Ravi, John ?) please correct me, but: Is the above not >> complete nonsense? I can't imagine poking around usefully in 10K >> dimensional space for an extremum unless maybe one can find the >> extremum by 10K separate 1-dim optimizations. And maybe not then >> either. >> >> Am I way offbase here, or has Brian merely described just another >> inefficient way to produce random numbers? >> >> -- Bert > > ______________________________________________ > 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. ______________________________________________ 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.