R help - Sep 2004 - maximization subject to constaint

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.

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.

 	-thomas

> 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