All Questions
Tagged with matrices oc.optimization-and-control
107 questions
1
vote
0
answers
221
views
Nonunique low-rank matrix completion from a few entries
Suppose we want to have a good approximation for the following NP-hard problem
$$\min_{\bf X} \operatorname{rank}({\bf X}) \text{ s.t. } \mathcal{A}({\bf X}) = {\bf b}, {\bf X} \succeq 0$$
where ${\bf ...
- 449
4
votes
2
answers
1k
views
Optimizing over matrices with spectral radius <1?
Suppose $F(x)$ is a convex objective function on $n\times n$ matrices, and I need to numerically optimize $F$ with the condition that $x$ has spectral radius less than $1$. This might be too hard, so ...
- 2,442
1
vote
0
answers
576
views
Minimizing quadratic form over permutations
Let $Q$ be an $n \times n$ real symmetric matrix and $x$ an $n \times 1$ real vector. Consider the following minimization problem:
$\min_{\pi \in S_n} ~(\pi x)^{\rm T} Q (\pi x)$,
where $S_n$ ...
- 1,839
2
votes
1
answer
1k
views
Condition number for Ellipsoid method matrix
Hello,
When using the ellipsoid method (for solving a linear program for example), the volume of the ellipsoid at each iteration is proven to decrease, and do so by at least a factor of $e^{1/2n}$.
...
- 88
3
votes
1
answer
1k
views
Maximize the multiplicity of an eigenvalue
Hi,
We have a real, non-singular and symmetric matrix M of size n by n, with diagonal elements 0's. Its eigenvalues and eigenvectors are computed.
Now we wish to change its diagonal elements ...
6
votes
3
answers
3k
views
minimize the sum of absolute eigenvalues
Hi,
We have a real symmetric matrix M with diagonal elements 0's, the eigenvalues and eigenvectors of M are computed.
Now we wish to change its diagonal elements arbitrarily to minimize the sum of ...
3
votes
1
answer
1k
views
Matrix approximation
Let A be an $m\times n$ matrix and $k$ be an integer. Assume that $A$ is non-negative. We want to find a scalar $\epsilon$ and an $n\times n$ matrix $B$ such that $A\leq A(\epsilon I + B)$ (where $\...
- 145