[R] maximization subject to constaint

Thomas Lumley tlumley at u.washington.edu
Tue Sep 14 11:01:56 CEST 2004

On Mon, 13 Sep 2004, Shuangge Ma wrote:

constrOptim() will do this, but it isn't a particularly efficient 
algorithm when the number of constraints is large.


> Hello:
> I have been trying to program the following maximization problem and would
> definitely welcome some help.
> the target function: sum_{i} f(alpha, beta'X_{i}),
>                     where alpha and beta are unknown d-dim parameter,
>                     f is a known function an X_{i} are i.i.d. r.v.
> I need to maximize the above sum, under the constaint that:
>                     beta'X_{i}+alpha<=1, for i=1,...,n.
> For one dimension, it is kind of trivial. What should I do with high
> dimensional alpha and beta?  Thanks for your time,
> Shuangge Ma, Ph.D.
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Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle

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