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Results tagged with semidefinite-programming
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user 121692
Semidefinite programming can be regarded as an extension of linear programming. In a semidefinite program, the goal is to optimize a linear function over the intersection of the cone of positive semidefinite matrices with some affine space.
4
votes
1
answer
231
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Convex Hull of Outer Products of (Normalised) Nonnegative Vectors
If I define $\mathcal{A} = \{ xx^T : x \in \mathbb{R}^d, \| x \|_2 \leqslant 1 \}$, then (assuming I recall correctly) it is known that the convex hull of $\mathcal{A}$ is given by
\begin{align}
\tex …
- 801
1
vote
2
answers
64
views
Monotonicity of kernel matrices with respect to hyperparameters
Let $\mathcal{X}$ be some nice space, let $\Phi$ be some ordered space, and let $K :\mathcal{X} \times \mathcal{X} \times \Phi \to \mathbf{R}$ be a positive-semidefinite kernel indexed by a hyperparam …
- 801
0
votes
Monotonicity of kernel matrices with respect to hyperparameters
An example which occurred to me is the following: suppose that $K$ indexes a family of stationary kernels (on e.g. $\mathbf{R}^d$) whose Fourier transforms are ordered pointwise. Following e.g. the pr …
- 801