## 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 ...

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 ...

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\...

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 ...

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=...

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