[R] question about constraint minimization

[Ravi Varadhan]

I do not understand the constraint x1 = x3 = x4.  If this is correct, you
only have 10 unknown parameters.

If you can correctly formulate your problem, you can have a look at the
packages "alabama" or "BB".  The function `auglag' in "alabama" or the
function `spg' in "BB" may be useful.

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 dhacademic at gmail.com
Sent: Monday, November 22, 2010 11:10 AM
To: r-help at r-project.org
Subject: Re: [R] question about constraint minimization


Hi,

I have struggled on this "bound optimization with equality constraint" by
using optim function for two days, but still fail to prepare a good input.
Can anyone help to prepare the input for my specific case? Many thanks.

Best,
Hao


On Sat, Nov 20, 2010 at 3:17 AM, Hans W Borchers [via R] <
ml-node+3051338-309339578-202837 at n4.nabble.com<ml-node%2B3051338-309339578-2
02837 at n4.nabble.com>
> wrote:

> dhacademic <at> gmail.com <dhacademic <at> gmail.com> writes:
>
> >
> >
> > Hi,
> >
> > I am a beginner of R. There is a question about constraint minimization.
> A
> > function, y=f(x1,x2,x3....x12), needs to be minimized. There are 3
> > requirements for the minimization:
> >
> > (1) x2+x3+...+x12=1.5 (x1 is excluded);
> > (2) x1=x3=x4;
> > (3) x1, x3 and x5 are in the range of -1~0, respectively. The rest
> variables
> > (x2, x4, x6, x7, ...., x12) are in the range of 0~1, respectively.
> >
> > The "optim" function is used. And part of my input is as follow, where
> > "xx1r" represents the x12:
> >
> > xx1r=1.5-x[2]-x[1]-x[1]-x[3]-x[4]-x[5]-x[6]-x[7]-x[8]-x[9]
> > start=rnorm(9)
> > up=1:9/1:9*1
> > lo=1:9/1:9*-1
> > out=optim(start,f,lower=lo,upper=up,method="L-BFGS-B",hessian=TRUE,
> > control=list(trace=6,maxit=1000))
> >
> > There are two problems in this input. the "up" and "lo" only define a
> range
> > of -1~1 for x1 to x11, which can not meet the requirement (3). In
> addition,
> > there is not any constraint imposed on x12. I have no idea how to
specify
> a
> > matrix that can impose different constraints on individual variables in
a
>
> > function. Any suggestion is highly appreciated.
> >
> > Best,
> > Hao
> >
>
> I don't see any direct need for real 'constraint' optimization here,
> it is a 'bounded' optimization where you are allowed to use
>
>     lower <- c(-1,0,-1,0,-1,0,0,0,0,0,0,0)
>     upper <- c( 0,1, 0,0, 0,1,1,1,1,1,1,1)
>
> Otherwise, your description is confusing:
>   (1) Did you change f to a new function with 9 variables, eliminating
>       x3, x4, and x12 ?
>   (2) x4 (being equal to x1) has to be in [-1, 0] but also in [0, 1]?
>   (3) If you need to restrict x12 to [0, 1] also, you cannot eliminate it.
>       Either keep x12 and use an equality constraint, or use inequality
>       constraints on xxlr.
>
> Hans Werner
>
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