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math.OC2026
On convergence rates of subgradient descent on semialgebraic functions
Evgenii Chzhen, Sholom Schechtman
We analyze the constant step size subgradient method on nonsmooth, nonconvex functions. We identify geometric assumptions on the objective function under which i) its domain admits…
math.OC2026
The gradient's limit of a definable family of functions admits a variational stratification
Sholom Schechtman
It is well-known that the convergence of a family of smooth functions does not imply the convergence of its gradients. In this work, we show that if the family is definable in an o…