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arXiv · 2607.24120

On the hardness of deterministic second-order optimization of functions with Lipschitz gradients

Jiewen Guan·Anthony Man-Cho So
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Abstract

We show that no deterministic zero-respecting algorithm (resp., (general) deterministic algorithm) can compute Goldstein approximate second-order stationary points of functions with Lipschitz continuous gradients within a finite number of (resp., no more than $n-3$ with $n$ being the input dimension) second-order oracle calls. This, among other consequences, shows that deterministic second-order weakly convex optimization is intractable.

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Jiewen Guan, Anthony Man-Cho So. 2026-07-27. On the hardness of deterministic second-order optimization of functions with Lipschitz gradients. https://arxiv.org/abs/2607.24120

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