All Questions

Is there a closed-form solution for $$\max_D \operatorname{Tr}(ADBD)$$ where $D$ is a $N\times N$ diagonal matrix with $m<N$ number of $1$'s and the rest are $0$'s, and $A$ and $B$ are real ...

Given $m,n,\ell\in\Bbb N$ and $\beta\in(0,1)$ consider the uniformly picked random matrix $A\in\Bbb Z^{n\times (n+1)}$ with $0\neq|\mathsf{det}(A^\circ)|\leq m^{\frac 1\ell}$ where $A^\circ$ is the ...

Consider the following linear program: $\left\{ \begin{array}{l} \underset{x}{max} \;\;c^Tx\\ [I, \;B]x = \mathbf{1}\\ x\geq 0 \end{array} \right.$ where $c$ is a vector ...