Author

Fang-Qing Zhang

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Preprint Oct 2026

Matching Full-Hessian Oracle Complexity for Nonconvex--Strongly-Concave Minimax Optimization

We characterize the oracle complexity of finding first-order stationary points in smooth nonconvex--strongly-concave (NC--SC) minimax optimization when each query provides the full Hessian in addition to the function value and gradient. For $\Phi(x)=\max_y f(x,y)$, assume that $f$ has an $L$-Lipschitz gradient, a $\rho...

Fang-Qing Zhang, Hai-Han Zhang, Wen-Dao Wu et al. · 0 citations

Preprint Oct 2026

Matching Randomized First-Order Bounds for Higher-Order Smooth Nonconvex Optimization

Does randomization improve the worst-case first-order complexity of nonconvex optimization when the objective is very smooth? We prove that, for every fixed finite integer $p\ge3$, finding an $\eps$-stationary point requires $\Omega_p(\eps^{-5/3})$ exact value-and-gradient queries, even for $C^\infty$ objectives with i...

Hai-Han Zhang, Wen-Dao Wu, Fang-Qing Zhang et al. · 0 citations