[R] BFGS versus L-BFGS-B

[Ravi Varadhan]

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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