Re: [R] Optimization problem with nonlinear constraint
For those interested in esoteric of special functions, here is a nice
reference on the Lambert W function:
http://www.cs.uwaterloo.ca/research/tr/1993/03/W.pdf
Ravi.
-Original Message-
From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On
Behalf Of Hans W Borchers
Sent: Wednesday, July 28, 2010 11:11 AM
To: r-h...@stat.math.ethz.ch
Subject: Re: [R] Optimization problem with nonlinear constraint
Uli Kleinwechter uni-hohenheim.de> writes:
>
> Dear Ravi,
>
> As I've already written to you, the problem indeed is to find a solution
> to the transcendental equation y = x * T^(x-1), given y and T and the
> optimization problem below only a workaround.
I don't think optimization is the right approach for simply inverting
a simple function.
The inverse of the function x \to x * e^x is the Lambert W function.
So the solution in your case is:
W(log(T)*y*T) / log(T) # hope I transformed it correctly.
Now, how to compute Lambert's W ? Well, look into the 'gsl' package
and, alas, there is the function lambert_W0.
Your example:
y <- 3
T <- 123
library(gsl)
lambert_W0(log(T)*y*T)/log(T)
# [1] 1.191830
Regards, Hans Werner
>
> John C. Nash has been so kind to help me on here. In case anyone faces a
> similar problem in the future, the solution looks as follows:
>
> *
>
> func1 <- function(y,x,T){
> out <- x*T^(x-1)-y
> return(out)
> }
>
> # Assign the known values to y and T:
> y <- 3
> T <- 123
>
> root <- uniroot(func1,c(-10,100),y=y,T=T)
> print(root)
>
>
>
> Somewhat simpler than I thought
>
> Thanks again!
>
> Uli
>
__
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
__
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Re: [R] Optimization problem with nonlinear constraint
Very nice, Hans! I didn't know of the existence of Lambert W function
(a.k.a Omega function) before. I didn't know that it occurs in the solution
of exponential decay with delay: dy/dy = a * y(t - 1). Apparently it is
more than 250 years old!
Thanks,
Ravi.
-Original Message-
From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On
Behalf Of Hans W Borchers
Sent: Wednesday, July 28, 2010 11:11 AM
To: r-h...@stat.math.ethz.ch
Subject: Re: [R] Optimization problem with nonlinear constraint
Uli Kleinwechter uni-hohenheim.de> writes:
>
> Dear Ravi,
>
> As I've already written to you, the problem indeed is to find a solution
> to the transcendental equation y = x * T^(x-1), given y and T and the
> optimization problem below only a workaround.
I don't think optimization is the right approach for simply inverting
a simple function.
The inverse of the function x \to x * e^x is the Lambert W function.
So the solution in your case is:
W(log(T)*y*T) / log(T) # hope I transformed it correctly.
Now, how to compute Lambert's W ? Well, look into the 'gsl' package
and, alas, there is the function lambert_W0.
Your example:
y <- 3
T <- 123
library(gsl)
lambert_W0(log(T)*y*T)/log(T)
# [1] 1.191830
Regards, Hans Werner
>
> John C. Nash has been so kind to help me on here. In case anyone faces a
> similar problem in the future, the solution looks as follows:
>
> *
>
> func1 <- function(y,x,T){
> out <- x*T^(x-1)-y
> return(out)
> }
>
> # Assign the known values to y and T:
> y <- 3
> T <- 123
>
> root <- uniroot(func1,c(-10,100),y=y,T=T)
> print(root)
>
>
>
> Somewhat simpler than I thought
>
> Thanks again!
>
> Uli
>
__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
Re: [R] Optimization problem with nonlinear constraint
Uli Kleinwechter uni-hohenheim.de> writes:
>
> Dear Ravi,
>
> As I've already written to you, the problem indeed is to find a solution
> to the transcendental equation y = x * T^(x-1), given y and T and the
> optimization problem below only a workaround.
I don't think optimization is the right approach for simply inverting
a simple function.
The inverse of the function x \to x * e^x is the Lambert W function.
So the solution in your case is:
W(log(T)*y*T) / log(T) # hope I transformed it correctly.
Now, how to compute Lambert's W ? Well, look into the 'gsl' package
and, alas, there is the function lambert_W0.
Your example:
y <- 3
T <- 123
library(gsl)
lambert_W0(log(T)*y*T)/log(T)
# [1] 1.191830
Regards, Hans Werner
>
> John C. Nash has been so kind to help me on here. In case anyone faces a
> similar problem in the future, the solution looks as follows:
>
> *
>
> func1 <- function(y,x,T){
> out <- x*T^(x-1)-y
> return(out)
> }
>
> # Assign the known values to y and T:
> y <- 3
> T <- 123
>
> root <- uniroot(func1,c(-10,100),y=y,T=T)
> print(root)
>
>
>
> Somewhat simpler than I thought
>
> Thanks again!
>
> Uli
>
__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
Re: [R] Optimization problem with nonlinear constraint
Dear Ravi,
As I've already written to you, the problem indeed is to find a solution
to the transcendental equation y = x * T^(x-1), given y and T and the
optimization problem below only a workaround.
John C. Nash has been so kind to help me on here. In case anyone faces a
similar problem in the future, the solution looks as follows:
*
func1 <- function(y,x,T){
out <- x*T^(x-1)-y
return(out)
}
# Assign the known values to y and T:
y <- 3
T <- 123
root <- uniroot(func1,c(-10,100),y=y,T=T)
print(root)
Somewhat simpler than I thought
Thanks again!
Uli
Am 26.07.2010 17:44, schrieb Ravi Varadhan:
Hi Uli,
I am not sure if this is the problem that you really want to solve. The
answer is the solution to the equation y = x * T^(x-1), provided a solution
exists. There is no optimization involved here. What is the real problem
that you are trying to solve?
If you want to solve a more meaningful constrained optimization problem, you
may want to try the "abalama" package which I just put on CRAN. It can
optimize smooth nonlinear functions subject to linear and nonlinear equality
and inequality constraints.
http://cran.r-project.org/web/packages/alabama/index.html
Let me know if you run into any problems using it.
Best,
Ravi.
-Original Message-
From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On
Behalf Of Uli Kleinwechter
Sent: Monday, July 26, 2010 10:16 AM
To: r-help@r-project.org
Subject: [R] Optimization problem with nonlinear constraint
Dear all,
I'm looking for a way to solve a simple optimization problem with a
nonlinear constraint. An example would be
max x s.t. y = x * T ^(x-1)
where y and T are known values.
optim() and constrOptim() do only allow for box or linear constraints,
so I did not succedd here. I also found hints to donlp2 but this does
not seem to be available anymore.
Any hints are welcome,
Uli
__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
Re: [R] Optimization problem with nonlinear constraint
Hi Uli, I am not sure if this is the problem that you really want to solve. The answer is the solution to the equation y = x * T^(x-1), provided a solution exists. There is no optimization involved here. What is the real problem that you are trying to solve? If you want to solve a more meaningful constrained optimization problem, you may want to try the "abalama" package which I just put on CRAN. It can optimize smooth nonlinear functions subject to linear and nonlinear equality and inequality constraints. http://cran.r-project.org/web/packages/alabama/index.html Let me know if you run into any problems using it. Best, Ravi. -Original Message- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of Uli Kleinwechter Sent: Monday, July 26, 2010 10:16 AM To: r-help@r-project.org Subject: [R] Optimization problem with nonlinear constraint Dear all, I'm looking for a way to solve a simple optimization problem with a nonlinear constraint. An example would be max x s.t. y = x * T ^(x-1) where y and T are known values. optim() and constrOptim() do only allow for box or linear constraints, so I did not succedd here. I also found hints to donlp2 but this does not seem to be available anymore. Any hints are welcome, Uli -- Uli Kleinwechter Agricultural and Food Policy Group (420a) University of Hohenheim D-70593 Stuttgart E-mail: u.kleinwech...@uni-hohenheim.de __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
