minimize frobenius norm subject to rank condition
$begingroup$
I'm trying to solve the following problem:
Let A be (a, b) matrix. Given l < min ( a, b) , solve:
begin{align}
min_{rank(X)= l} || A - X ||_{Fro}^2
end{align}
I'm novice in optimization and don't know how to take the rank constraint into account.
Thanks!
optimization convex-optimization
asked Dec 6 '18 at 9:28
Lu YinLu Yin
183
$endgroup$
add a comment |
$begingroup$
I'm trying to solve the following problem:
Let A be (a, b) matrix. Given l < min ( a, b) , solve:
begin{align}
min_{rank(X)= l} || A - X ||_{Fro}^2
end{align}
I'm novice in optimization and don't know how to take the rank constraint into account.
Thanks!
optimization convex-optimization
asked Dec 6 '18 at 9:28
Lu YinLu Yin
183
$endgroup$
add a comment |
$begingroup$
I'm trying to solve the following problem:
Let A be (a, b) matrix. Given l < min ( a, b) , solve:
begin{align}
min_{rank(X)= l} || A - X ||_{Fro}^2
end{align}
I'm novice in optimization and don't know how to take the rank constraint into account.
Thanks!
optimization convex-optimization
asked Dec 6 '18 at 9:28
Lu YinLu Yin
183
$endgroup$
I'm trying to solve the following problem:
Let A be (a, b) matrix. Given l < min ( a, b) , solve:
begin{align}
min_{rank(X)= l} || A - X ||_{Fro}^2
end{align}
I'm novice in optimization and don't know how to take the rank constraint into account.
Thanks!
optimization convex-optimization
optimization convex-optimization
asked Dec 6 '18 at 9:28
Lu YinLu Yin
183
asked Dec 6 '18 at 9:28
Lu YinLu Yin
183
edited Dec 6 '18 at 9:43
Lu Yin
asked Dec 6 '18 at 9:28
Lu YinLu Yin
183
asked Dec 6 '18 at 9:28
Lu YinLu Yin
183
asked Dec 6 '18 at 9:28
Lu YinLu Yin
183
183
add a comment |
add a comment |
1 Answer
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$begingroup$
As a generic optimization problem, it is a very hard problem since rank constraints typically are intractable.
However, this particular problem has an analytic solution in terms of the SVD
https://en.wikipedia.org/wiki/Low-rank_approximation
answered Dec 6 '18 at 13:19
Johan LöfbergJohan Löfberg
5,2551811
$endgroup$
add a comment |
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1 Answer
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1 Answer
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active
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$begingroup$
As a generic optimization problem, it is a very hard problem since rank constraints typically are intractable.
However, this particular problem has an analytic solution in terms of the SVD
https://en.wikipedia.org/wiki/Low-rank_approximation
answered Dec 6 '18 at 13:19
Johan LöfbergJohan Löfberg
5,2551811
$endgroup$
add a comment |
$begingroup$
As a generic optimization problem, it is a very hard problem since rank constraints typically are intractable.
However, this particular problem has an analytic solution in terms of the SVD
https://en.wikipedia.org/wiki/Low-rank_approximation
answered Dec 6 '18 at 13:19
Johan LöfbergJohan Löfberg
5,2551811
$endgroup$
add a comment |
$begingroup$
As a generic optimization problem, it is a very hard problem since rank constraints typically are intractable.
However, this particular problem has an analytic solution in terms of the SVD
https://en.wikipedia.org/wiki/Low-rank_approximation
answered Dec 6 '18 at 13:19
Johan LöfbergJohan Löfberg
5,2551811
$endgroup$
As a generic optimization problem, it is a very hard problem since rank constraints typically are intractable.
However, this particular problem has an analytic solution in terms of the SVD
https://en.wikipedia.org/wiki/Low-rank_approximation
answered Dec 6 '18 at 13:19
Johan LöfbergJohan Löfberg
5,2551811
answered Dec 6 '18 at 13:19
Johan LöfbergJohan Löfberg
5,2551811
answered Dec 6 '18 at 13:19
Johan LöfbergJohan Löfberg
5,2551811
answered Dec 6 '18 at 13:19
Johan LöfbergJohan Löfberg
5,2551811
5,2551811
add a comment |
add a comment |
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