s***n
发帖数: 9499 | 1 Minimize Trace((A'A)^(-1)),
Where variable A is an n by n real matrix, and every element of the matrix A
is between 0 and 1.
A' denotes the transpose of A.
^(-1) denotes the inverse of a matrix.
Any suggestions or references are highly appreciated! |
B********e
发帖数: 10014 | 2 问题在哪？
to find a matrix...?
A
【在 s***n 的大作中提到】
: Minimize Trace((A'A)^(-1)),
: Where variable A is an n by n real matrix, and every element of the matrix A
: is between 0 and 1.
: A' denotes the transpose of A.
: ^(-1) denotes the inverse of a matrix.
: Any suggestions or references are highly appreciated!
|
s*****s
发帖数: 20 | 3 同问
AA^t is symmetric and thus can be diagonalized.
【在 B********e 的大作中提到】
: 问题在哪？
: to find a matrix...?
:
: A
|
k****n
发帖数: 81 | 4 if A'A is nonsigular, then you can try cholesky decomposition. maybe that
will help you some.
A
【在 s***n 的大作中提到】
: Minimize Trace((A'A)^(-1)),
: Where variable A is an n by n real matrix, and every element of the matrix A
: is between 0 and 1.
: A' denotes the transpose of A.
: ^(-1) denotes the inverse of a matrix.
: Any suggestions or references are highly appreciated!
|
s***n
发帖数: 9499 | 5 是的
To find a matrix A.
Any suggestions?:)
【在 B********e 的大作中提到】
: 问题在哪？
: to find a matrix...?
:
: A
|
s***n
发帖数: 9499 | 6 Yes.
Actually it is easy to prove the object function
tr((A'A)^(-1)) is equal to the sum of one over single value square of A.
What I need is an effcient way to find the optimal A.
【在 s*****s 的大作中提到】
: 同问
: AA^t is symmetric and thus can be diagonalized.
|
s***n
发帖数: 9499 | 7 thanks:)
But it looks like I didn't state my question clearly. :)
argmin{tr((A'A)^(-1))}
A
Where 0<= Aij <=1.
Invertible also implies A is full rank.
Let A be a n by n matrix.
I know the result for n = 1, 3, 7, 11, ... (4k-1)
For example, when n = 3,
A =
[
0 1 1
1 0 1
1 1 0
],
which is related to Hadamard matrix for n+1 = 2, 4, 8, 12, ...(4k).
I would be appreciate if you can give some hints for other values of n such
as 4, 5, 6. |
s***n
发帖数: 9499 | 8 Is it a convex optimization problem?
Or any approximation to transform it to a convex optimization problem?
【在 s***n 的大作中提到】
: thanks:)
: But it looks like I didn't state my question clearly. :)
: argmin{tr((A'A)^(-1))}
: A
: Where 0<= Aij <=1.
: Invertible also implies A is full rank.
: Let A be a n by n matrix.
: I know the result for n = 1, 3, 7, 11, ... (4k-1)
: For example, when n = 3,
: A =
|
D*******a
发帖数: 3688 | 9 好像SDP基本都是用内点法吧
【在 s***n 的大作中提到】
: Yes.
: Actually it is easy to prove the object function
: tr((A'A)^(-1)) is equal to the sum of one over single value square of A.
: What I need is an effcient way to find the optimal A.
|
s***n
发帖数: 9499 | 10 Why is it a SDP problem?
We have an inverse here.
【在 D*******a 的大作中提到】
: 好像SDP基本都是用内点法吧
|
D*******a
发帖数: 3688 | 11 i know, but I speculate interior point method may still work
have you tried that?
【在 s***n 的大作中提到】
: Why is it a SDP problem?
: We have an inverse here.
|
s***n
发帖数: 9499 | 12 Thanks. Not yet. I'm not sure how good the interior point is for a non-conve
x problem.
Which software do you suggest for the implementation of interior point metho
d?
How about integer programming? Which software?
Coz it is more important to know the result for
Aij = 0 or 1.
【在 D*******a 的大作中提到】
: i know, but I speculate interior point method may still work
: have you tried that?
|
D*******a
发帖数: 3688 | 13 i think you can serialize the variables and make it an MINLP
then there are some solvers available, e. g. MINLPBB, BARON...
conve
metho
【在 s***n 的大作中提到】
: Thanks. Not yet. I'm not sure how good the interior point is for a non-conve
: x problem.
: Which software do you suggest for the implementation of interior point metho
: d?
: How about integer programming? Which software?
: Coz it is more important to know the result for
: Aij = 0 or 1.
|
s***n
发帖数: 9499 | 14 cool!
I will try the one with Branch and Bound for the integer constraints. If the
re is any interesting result, I will let your guys know.
【在 D*******a 的大作中提到】
: i think you can serialize the variables and make it an MINLP
: then there are some solvers available, e. g. MINLPBB, BARON...
:
: conve
: metho
|
