We study the problem of decomposing a polynomial p into a sum of r squares by minimizing a quadratically penalized objective f p(u) = || ∑r i=1 u2i-p||2. This objective is nonconvex and is equiva…
This paper presents a selected tour through the theory and applications of lifts of convex sets. A lift of a convex set is a higher-dimensional convex set that projects onto the original set. Many …
We revisit Min-Mean-Cycle, the classical problem of finding a cycle in a weighted directed graph with minimum mean weight. Despite an extensive algorithmic literature, previous work failed to achie…