R help - Aug 2008 - nonlinear constrained optimization

Hi.  I need some advises on how to use R to find pi (i is the index) with
   the following objective function and constraint:

   max (sum i)[ f(ai, bi, pi) * g(ci, di, pi) * Di ]

   s.t.  (sum i)[ f(ai, bi, pi) * Di * pi] / (sum i)[ f(ai, bi, pi) * Di ]  <
constant

   f and g are diffentiable.
   So, I am thinking of optim with method = "BFGS"? But wonder how to
include
   the constraint.
   I also saw constrOptim but it says for linear constraint only.
   So, what will be the suitable function to use then?
   Also, how should I write (sum i) in R?
   Many thanks and your help is much appreciated.
   ----
   Chua Siang Li
   Consultant - Operations Research
   Acceval Pte Ltd
   Tel: 6297 8740
   Email: siang.li.chua at acceval-intl.com
   Website: www.acceval-intl.com
   This message and any attachments (the "message"...{{dropped:13}}

On Tue, Aug 19, 2008 at 8:35 AM, Chua Siang Li
<siang.li.chua at acceval-intl.com> wrote:
>
>   Hi.  I need some advises on how to use R to find pi (i is the index) with
>   the following objective function and constraint:
>
>   max (sum i)[ f(ai, bi, pi) * g(ci, di, pi) * Di ]
>
>   s.t.  (sum i)[ f(ai, bi, pi) * Di * pi] / (sum i)[ f(ai, bi, pi) * Di ] 
<>   constant
>
>   f and g are diffentiable.
>   So, I am thinking of optim with method = "BFGS"? But wonder how
to include
>   the constraint.
>   I also saw constrOptim but it says for linear constraint only.
>   So, what will be the suitable function to use then?
>   Also, how should I write (sum i) in R?
>   Many thanks and your help is much appreciated.
Up to my best knowledge, R cannot deal with optimization problems with
nonlinear constraints, unless one uses the penalty method. Outside R,
Ipopt and Algencan can solve problems like yours, but one needs to
program in AMPL and/or C/Fortran.

Paul