# Tag Info

### 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 ...
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 ...

### 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\...
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 ...
$\newcommand\R{\mathbb R}\newcommand\b{\hat\rho(x)}\newcommand\a{\tilde\rho(x)}$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=...