7 problems

AMP optimality conjecture. AMP algorithms are optimal for average-case sparse optimization problems.

Let $\mu_1 \in \mathcal{D}_+(S^1)$ be a finitely supported, non-negative measure. For the unit ball $\mathcal{B}_1(\mu_1)$ and its extreme points…

A probability vector is sparsified by solving an $\ell_0$-regularized separable Bregman projection problem over the simplex; the resulting primitive admits exact and efficient opti…

Generic 2n-support conjecture. Generically, the support set $\Omega$ needs at least $2n$ elements: one per column to satisfy…

For users indexed by $k$, let $mathcal{N}(k)={i:lVert bm{x}k-bm{x}irVert<r}$ be the neighbor set determined by device locations, and let the GLASSO groups be the neighbor sets…

Local-minima conjecture. For the regularized LQRm problem there are at most two local minima: one associated with the LQRm cost and one associated with the regularization, which te…

Let $\tau$ denote the optimization error appearing in Theorem. Optimization-error conjecture. It should be possible to remove the term $\tau$ from the theorem's bound. The conjectu…