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Results tagged with convex-analysis
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user 169474
1
vote
How to prove this (corollary of) hyperplane separation theorem?
I thought that I had an answer for both part, but for the moment, I succeed only on the first part, which is an application of the first separation theorem given in
https://en.wikipedia.org/wiki/Hyper …
- 3,808
2
votes
Accepted
Smooth approximation of nonnegative, nondecreasing, concave functions
Replace the convolution on $\mathbb{R}$ by a convolution on the group $\mathbb{R}_+^*$, endowed with the invariant measure $dx/x$, namely set
$$f_n(x) := \int_0^\infty \varphi_n(y) f(x/y) \frac{dy}{y} …
- 3,808
2
votes
Convex functions in convex sets
Not an answer, but a too long remark for a comment.
The property holds for any Euclidean ball. By translation one may assume that the center is $0$. Call R the radius. Then the volume is $b_nR^n$ and …
- 3,808