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math.OC2026
On computing Goldstein approximate second-order stationary points of structured nonsmooth nonconvex programs
Jiewen Guan, Anthony Man-Cho So
In this paper, we exhibit a randomized first-order algorithm to compute Goldstein approximate second-order stationary points of -smooth functions, using tools from randomized sm…
math.OC2026
On the hardness of deterministic second-order optimization of functions with Lipschitz gradients
Jiewen Guan, Anthony Man-Cho So
We show that no deterministic zero-respecting algorithm (resp., (general) deterministic algorithm) can compute Goldstein approximate second-order stationary points of functions wit…