5 problems

Let $f$ be a block-structured objective with an exact minimization available over each block. Suppose an accelerated alternating minimization method has convergence rate $O(1/k^2)$…

Alternating minimization conjecture. The algorithm with random initialization succeeds when

Waldspurger's conjecture. The algorithm succeeds with high probability when

Let the phase-retrieval observations be $y_i=|\boldsymbol{a}_i^*\boldsymbol{z}|$ for $i=1,2,\ldots,m$, where $\boldsymbol{z}\in\mathbb{C}^n$ is the underlying signal and the observ…

Let $n$ be the signal dimension and let $\frac{1}{\epsilon^2}$ denote the accuracy-dependent sample-complexity scale for one-bit phase retrieval. Consider alternating minimization…