R help - Apr 2004 - constrOptim does ineq, not eq, but who do ?

Hi everybody,

please, could you give me help ? I scanned the help archives and didn't
found hints...

I want to solve a large sparse linear system subjected to an inequality
constrains (all solutions positive) and an equality constrain (all
solutions sum to 1), thus I tried to fool constrOptim using:

 x[1] +   0  + ... +  0   >= 0
...
   0  +   0  + ... + x[n] >= 0
 x[1] + x[2] + ... + x[n] >= 1
-x[1] - x[2] - ... - x[n] >= -1

in minimization: min( dist(A*x - b) )

But, since the initial guess x0 must be in the fasiable region and NOT in
the boundaries (due to trick I only have boundary), this trick doens't
work out.

If constrOptim doesn't make subject to equalities, what function could do
this optimization ? any ideia ?

I look for something similar to MATLAB's lsqlin function:
http://web.media.mit.edu/~bill/workspace/matlab/toolbox/optim/lsqlin.html

Dear Ricardo,

Optimization of the surrogate function that is used in the constrOptim
under equality constraints can be implemented by applying the
lagrangian rule to the surrogate function (instead of using 'optim').

The iterative formula can be found in Lange, K. (1999). Numerical
analysis for statisticians. Springer-Verlag, New York. pp: 184.

I hope this helps.

Roula


----- Original Message ----- 
From: "Ricardo Zorzetto Nicoliello Vencio" <rvencio at
ime.usp.br>
To: <r-help at stat.math.ethz.ch>
Sent: Tuesday, April 27, 2004 1:59 PM
Subject: [R] constrOptim does ineq, not eq, but who do ?

> Hi everybody,
>
> please, could you give me help ? I scanned the help archives and
didn't
> found hints...
>
> I want to solve a large sparse linear system subjected to an
inequality
> constrains (all solutions positive) and an equality constrain (all
> solutions sum to 1), thus I tried to fool constrOptim using:
>
>  x[1] +   0  + ... +  0   >= 0
> ...
>    0  +   0  + ... + x[n] >= 0
>  x[1] + x[2] + ... + x[n] >= 1
> -x[1] - x[2] - ... - x[n] >= -1
>
> in minimization: min( dist(A*x - b) )
>
> But, since the initial guess x0 must be in the fasiable region and
NOT in
> the boundaries (due to trick I only have boundary), this trick
doens't
> work out.
>
> If constrOptim doesn't make subject to equalities, what function
could do
> this optimization ? any ideia ?
>
> I look for something similar to MATLAB's lsqlin function:
>
http://web.media.mit.edu/~bill/workspace/matlab/toolbox/optim/lsqlin.html
>
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