6 problems

Consider the sub-gradient method (SubGM) for robust matrix recovery, initialized either by a spectral method followed by norm reduction or by a small random initialization. Initial…

A semidefinite program is called primal simple when its primal optimal solution is unique. Primal simplicity conjecture. Primal simplicity should continue to hold for semidefinite-…

Let $X$ be an $M\times N$ matrix, let $\rho$ denote its asymptotic rank fraction, and let $\beta$ denote the aspect ratio. For singular value soft thresholding, write…

Recall that ${\mathcal M}_{d,r}({\mathbb F})$ denotes the set of $d\times d$ matrices over ${\mathbb F}$ with rank at most $r$. Let ${\mathcal A}=(A_j)_{j=1}^N$ be a collection of…

Let $\mathbf A_i$ be the sensing matrices, let $\mathbf X=\mathbf P\mathbf Q$ have joint sparsity level $k$ and rank $r$, and let $N$ be the number of observations. Writing…

Let $X$ be a rectangular matrix with repeated singular values, and let the directional derivative refer to the formula established in Theorem for the relevant matrix-valued spectra…