New answers tagged oc.optimization-and-control
4
votes
Is this constraint convex?
Rewrite the constraint as
$$x_n \le f_n(\rho_1,\dots,\rho_n):=\ln\Big(B\log_2\Big(1+\frac{e^{\rho_n} g_n^2}{\sum_{i=1}^{n-1} e^{\rho_i} g_i^2+\sigma^2}\Big)\Big).$$
The problem is then to prove the ...
- 110k
2
votes
Accepted
Convex optimization without Slater's condition
This is a partial answer, which addresses the practicalities of and workarounds for solving convex optimization problems not satisfying Slater's condition. It does not address the existence of a ...
- 1,432
2
votes
Estimating $\max_{\|u\|=1} \frac{ E\left[\langle u\cdot x\rangle ^4\right]}{E\left[\langle u\cdot x\rangle ^2\right]}$
$\newcommand\si\sigma\newcommand\Si\Sigma$If $x$ is centered, then $u\cdot x\sim N(0,\si_u^2)$, where $\si_u^2:=u\cdot\Si u$ and $\Si$ is the covariance matrix of $x$. So,
$$\frac{E(u\cdot x)^4}{E(u\...
- 110k
5
votes
How to get this inequality in Santambrogio's book about optimal transport?
Iosif already pointed out the trivial typo. For the purposes of the argument in that proof (incidentally, it requires that the objects be probability densities on a compact set $\Omega$, not on whole ...
- 35.3k
5
votes
Accepted
How to get this inequality in Santambrogio's book about optimal transport?
$\newcommand\R{\mathbb R}\newcommand\b{\hat\rho(x)}\newcommand\a{\tilde\rho(x)}$This inequality is false in general.
For instance, if $\varepsilon=1/10$, $M=1/10$, and for some $x\in\R^d$ we have $\a=...
- 110k
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