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arXiv · 2607.21258

A Gaussian smoothing-based zeroth-order method for Goldstein second-order stationarity

Ming Lei·Ting Kei Pong·Man-Chung Yue·Liaoyuan Zeng·Hao Zhang
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Abstract

We introduce a new generalized Hessian, called the Goldstein second-order $\delta$-subdifferential, and an associated notion of $(\epsilon_1,\epsilon_2,\delta)$-second-order stationary point for continuously differentiable functions with locally Lipschitz gradients. We propose a zeroth-order algorithm based on cubic regularization and Gaussian smoothing with homotopy to find such approximate second-order stationary points for Lipschitz differentiable functions, and derive the iteration complexity under a mild coercivity-type assumption on the objective function.

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Ming Lei, Ting Kei Pong, Man-Chung Yue, Liaoyuan Zeng, Hao Zhang. 2026-07-23. A Gaussian smoothing-based zeroth-order method for Goldstein second-order stationarity. https://arxiv.org/abs/2607.21258

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