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Results tagged with convex-analysis
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user 29697
7
votes
1
answer
416
views
Nondifferentiable convex function whose subdifferential admits a continuous selection
Is there a convex function $F$ that is not differentiable, but whose subdifferential admits a continuous selection, i.e. a continuous $g$ with $g(x) \in \partial F(x)$ for all $x$ in the domain?
In on …
- 4,529
4
votes
2
answers
697
views
Existence of a strictly convex function interpolating given gradients and values
I'm wondering where to find a proof and reference for the following facts, which I feel sure must be true.
(1) Suppose we are given a finite set of points in $\mathbb{R}^{d+1}$. For each point, we ar …
- 4,529
2
votes
Example of a (strictly) proper scoring rule on a general measurable space?
Well, it might be important to limit $\mathcal{P}$ here. If we consider the space $\Omega = \mathbb{R}$ with Lebesgue measure, we might take $\mathcal{P}$ to be the set of distributions with a continu …
- 4,529
3
votes
Example of a (strictly) proper scoring rule on a general measurable space?
Turns out that Gneiting and Raftery give an example in Section 4.2 of the continuous ranked probability score (CRPS), which is strictly proper for $\mathcal{P}$ equal to the Borel probability measures …
- 4,529