关于具有Lipschitz梯度函数的确定性二阶优化的难度
On the hardness of deterministic second-order optimization of functions with Lipschitz gradients
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中文总结 AI 辅助
研究具有Lipschitz梯度函数的确定性二阶优化难度，证明不存在能在有限二阶预言机调用内计算Goldstein近似二阶驻点的确定性算法，揭示确定性二阶弱凸优化难处理。
中文摘要 AI 辅助
我们证明，没有确定性的零尊重算法（相应地，（一般）确定性算法）能够在有限数量的（相应地，不超过输入维度\(n\)减\(3\)次）二阶预言机调用内计算出具有Lipschitz连续梯度函数的Goldstein近似二阶驻点。这表明确定性二阶弱凸优化是难处理的。
英文摘要
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.
