BFGS versus L-BFGS-B
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: rvaradhan at jhmi.edu -----Original Message----- From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of Prof. John C Nash Sent: Friday, February 25, 2011 5:55 PM To: Bert Gunter Cc: r-help at 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 <btsai00 at 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
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