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math.OC2022★ 16 cited
The effect of smooth parametrizations on nonconvex optimization landscapes
Eitan Levin, Joe Kileel, Nicolas Boumal
We develop new tools to study landscapes in nonconvex optimization. Given one optimization problem, we pair it with another by smoothly parametrizing the domain. This is either for…
math.OC2021★ 22 cited
Finding stationary points on bounded-rank matrices: A geometric hurdle and a smooth remedy
Eitan Levin, Joe Kileel, Nicolas Boumal
We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delic…