All Questions
Tagged with linear-programming semidefinite-programming
8 questions
2
votes
1
answer
227
views
Solving linear programming without solving linear programming
Let $v_1, \cdots, v_n$ be vectors in $\mathbb R^k$, and let $M$ be the Gram matrix of them.
It's possible to determine from $M$ and $k$ whether the only vector that has nonnegative inner product with ...
- 9,501
1
vote
0
answers
68
views
Fundamental regions in convex programming
In linear programming, the fundamental regions are polyhedra, since those are the intersection of half-spaces defined by linear inequalities. In semidefinite programming, the fundamental regions are ...
- 13.9k
1
vote
0
answers
82
views
What is the relation between different generalizations of linear programming?
Linear programming subsumed by each of
Semidefinite programming (SDP)
Convex programming (CXP)
SOS programming (SSP)
Is there any relation between each pair in the three?
Are all three equivalent in ...
- 1,826
2
votes
0
answers
148
views
Generalization of Farkas' Lemma to Hermitian Matrices
I recently stumbled upon a well-known version of Farkas' Lemma which, roughly speaking, I would like to generalize from real vectors to hermitian matrices, as it seems promising for something else I ...
3
votes
0
answers
178
views
Uniqueness of projection under spectral norm
I am considering
$$
\min_{M\in \mathcal{M}} \|X - M\|:=x \neq 0,
$$
where $X$, $M$ are $m\times n$ matrices, $\|\cdot\|$ is spectral norm and $\mathcal{M}$ is a matrix subspace. I wonder to what ...
- 131
3
votes
2
answers
1k
views
SDP relaxation vs LP relaxation
I have a question I hope you might be able to answer.
Let's say we have an integer program for the stable set problem (or clique, not principal).
\begin{equation}
\begin{aligned}
& \text{...
- 342
2
votes
1
answer
191
views
Optimization problem whose cardinality never exceeds 7 for some reason
I am working on a problem in which I have a collection of $n$ points, $x_1,\dots,x_n$, in the plane, as well as a positive definite matrix $\Sigma$ and another point $\mu$ in the plane. I am trying ...
35
votes
4
answers
5k
views
Why are optimization problems often called "programs"?
Why are optimization problems often called programs?
linear programming
geometric programming
convex programming
Integer programming
...
- 461