[R] Constrained Optimization, a full example

[Hesen Peng]

Hmmmm, I'm assuming that you are trying to find the solution of \beta
to the question:

argmin |y-X\beta|_2^2, which is a quadratic programming problem.

On Tue, Jun 16, 2009 at 6:29 PM, Hesen Peng<hesen.peng at gmail.com> wrote:
> Hello,
>
> Since the optimization goal is quadratic and constraint is linear,
> quadratic programming functions will help. There are many such
> packages available, e.g. quadprog.
>
> On Tue, Jun 16, 2009 at 5:54 PM, Stu @ AGS<stu at agstechnet.com> wrote:
>> After a few days of work, I think I nearly have it.
>>
>> Unfortunately, theta is unchanged after I run this (as a script from a
>> file).  I thought that theta would contain the fitted parameters.
>>
>>
>>
>> The goal here is to find the least squares fit according to the function
>> defined as "rss" subject to the constraints defined as ui and ci.
>>
>> I defined ui and ci to (hopefully) force par2 and par3 into the range  0.0
>> <= par2 <= 1.0 and 0.0 <= par3 <= 1.0.
>>
>> I am not at all sure that ui and ci are defined correctly.
>>
>>
>>
>> The call to constrOptim returns normally, but without a solution
>> (apparently).
>>
>>
>>
>> Any suggestions appreciated.
>>
>> Thanks
>>
>> Stu
>>
>>
>>
>> # data
>>
>> y <-
>> c(0.111111111111111,0.0921052631578947,0.0564516129032258,0.0608108108108108
>> ,0.0128205128205128,0.0136078431372549);
>>
>> x1 <-
>> c(0,0.978723404255319,0.087378640776699,0.549295774647887,0.0596026490066225
>> ,0.61578947368421);
>>
>> x2 <- c(1,3,4,5,6,7);
>>
>> x3 <- c(3600,169200,185400,255600,271800,342000);
>>
>>
>>
>> observs <- data.frame(y, x1, x2, x3);
>>
>>
>>
>> # function definition
>>
>> rss <- function(par, y, x1, x2, x3) {
>>
>>  par1 <- par[1]
>>
>>  par2 <- par[2]
>>
>>  par3 <- par[3]
>>
>>  ressq <- (y - par1 * (x1 + 1) * x2^(-par2) * x3^par3)^2
>>
>>  sum(ressq)
>>
>>  }
>>
>>
>>
>> #call to optimizer
>>
>> opti <- constrOptim(c(0.5, 0.5, 0.1), rss, NULL, ui = rbind(c(0, 0), c(1,
>> 0), c(0, 1)), ci = c(0, 1, 1));
>>
>>
>>
>>
>>        [[alternative HTML version deleted]]
>>
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>> and provide commented, minimal, self-contained, reproducible code.
>>
>
>
>
> --
> 彭河森 Hesen Peng
> http://hesen.peng.googlepages.com/
>



-- 
彭河森 Hesen Peng
http://hesen.peng.googlepages.com/