[R] How to formulate constraint like abs(x) = y in constrOptim (or other)

[Benjamin B.]

Thanks a lot for your responses.
Alabama and Rsolnp packages look promising.
My first tests worked well.

For others searching for alike problems I now use something like:

#equality constraint function
eqFkt<-function(x){
  #for sum(x)=sum_x
  sm<-sum(x)-sum_x
  return(c(sm))
}          
  
ineqFkt<-function(x){
  #for -max_x < x < max_x
  ubound    <- -x+max_x
  lbound    <- x+max_x
  #for sum of all negative value to be > min_x_neg
  negbound  <- sum(x[x<0])-min_x_neg
  return(c(ubound, lbound, negbound))
}  
                                  
#define start  
start_weights<-seq(0, 0, length.out=len_data)
#where mini_func is the minimizing function
res <-auglag(start_weights, mini_func, heq=eqFkt, hin=ineqFkt)

Benjamin

-----Ursprüngliche Nachricht-----
Von: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] Im
Auftrag von Ravi Varadhan
Gesendet: Montag, 6. Dezember 2010 23:53
An: 'Hans W Borchers'; r-help at stat.math.ethz.ch
Betreff: Re: [R] How to formulate constraint like abs(x) = y in constrOptim
(or other)

Hi Benjamin,

If you just had abs(x_i) < c_i, it will reduce to linear inequalities, but
your constraint cannot be reduced to that.

You might try "alabama" or "Rsolnp" packages.

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 Hans W Borchers
Sent: Monday, December 06, 2010 1:08 PM
To: r-help at stat.math.ethz.ch
Subject: Re: [R] How to formulate constraint like abs(x) = y in constrOptim
(or other)

Benjamin B. <benj.bad.ac <at> googlemail.com> writes:

> Hello list reader,
> 
> I am trying to form some constraints for an optimization I am working on.
> I think I have understand the use of the constraints in matrix form. I use
> them like:
> 
> [...]
> 
> Now I would like to formulate a constraint like
> 
> Sum(Abs(x_i))<=limit
> 
> But I have no idea how I could get such a condition by using the matrix
> constraint formulation.
> 
> I have already searched the help, web and all searchable R resources I
could
> find, but got no helping result.
> 
> Is constrOptim the right function to use?
> 
> Maybe you can give me a hint or can point me to a good description of
> constraint handling.
> 
> Greetings and thanks in advance,
> 
> Benjamin
> 
> Benjamin B.
> Hamburg, Germany

With 'constrOptim' you can formulate linear constraints only, and in most
cases abs() is not linear. You might try one of the nonlinear optimization
packages.

Another possibility is to reformulate the absolute value with two binary
values, if your optimization function itself is linear; you didn't tell us
the whole story.

Hans Werner

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