optimization problem
Yes, it can be formulated as an LSAP. It works just fine. I have checked it with several 3 x 3 examples. Here is another convincing example: n <- 50 A <- matrix(rnorm(n*n), n, n)
# Find P such that ||PA - C|| is minimum
vec <- sample(1:n, n, rep=FALSE) # a random permutation C <- A[vec, ] # the target matrix is just a permutation of original matrix B <- pMatrix.min(A, C)$A
dist(B, C)
[1] 0
dist(A, C)
[1] 69.60859 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: Erwin Kalvelagen <erwin.kalvelagen at gmail.com> Date: Saturday, January 16, 2010 1:36 pm Subject: Re: [R] optimization problem To: Ravi Varadhan <rvaradhan at jhmi.edu> Cc: r-help at stat.math.ethz.ch
I also have doubts this can be formulated correctly as a linear assignment problem. You may want to check the results with a small example. Erwin ---------------------------------------------------------------- Erwin Kalvelagen Amsterdam Optimization Modeling Group erwin at amsterdamoptimization.com ---------------------------------------------------------------- On Sat, Jan 16, 2010 at 9:59 AM, Ravi Varadhan <rvaradhan at jhmi.edu> wrote:
Thanks, Erwin, for pointing out this mistake.
Here is the correct function for Frobenius norm.
Klaus - Just replace the old `dist' with the following one.
dist <- function(A, B) {
# Frobenius norm of A - B
n <- nrow(A)
sqrt(sum((B - A)^2))
}
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: Erwin Kalvelagen <erwin.kalvelagen at gmail.com>
Date: Saturday, January 16, 2010 2:35 am
Subject: Re: [R] optimization problem
To: r-help at stat.math.ethz.ch
Ravi Varadhan <rvaradhan <at> jhmi.edu> writes:
dist <- function(A, B) {
# Frobenius norm of A - B
n <- nrow(A)
sum(abs(B - A))
}
See for a definition of the
Frobenius norm.
Erwin
----------------------------------------------------------------
Erwin Kalvelagen
Amsterdam Optimization Modeling Group
erwin at amsterdamoptimization.com
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