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Results tagged with inequalities
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user 9652
for questions involving inequalities, upper and lower bounds.
12
votes
Accepted
Convexity and Lipschitz continuity
That's a standard result in convex optimization. For example Theorem 2.1.5 in Nesterov's "Introductory Lectures on Convex Optimization" states that the following are equivalent:
$f$ is $C^1$, convex …
- 12.7k
5
votes
Accepted
A corollary of Gibbs' inequality
That does not seem to be true. Here is how you can build a counterexample: Define $F(q) = \sum_i q_i^{p_i} - p_i^{p_i}$ and note that $F(p)=0$. To find $q$ such that $F(q)> 0$ try to set $\tilde q = p …
- 12.7k
6
votes
Identities and inequalities in analysis and probability
.$$
This include Cauchy-Schwarz and Young's inequality but can sometimes be used to get more specific inequalities. …
3
votes
2
answers
1k
views
Do you know this form of an uncertainty principle?
The last fact bothers me: In contrast to the fact that both inequalities can be derived from two conceptually very different integral transforms (indeed both underlying groups are very different), they … Is there some reason why these inequalities seem so entangled? …
- 12.7k