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arXiv · 2607.23863

Polynomial-time computation of $\ell_p$-contraction fixed points for even $p$

Constantinos Daskalakis·Gabriele Farina·Brian Hu Zhang
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Abstract

We give a $\text{poly}(d, p, \log(1/\epsilon))$-time algorithm that computes an $\epsilon$-approximate fixed point of any $\ell_p$-nonexpansive map $f : \mathcal{X} \to \mathcal{X}$, where $\mathcal{X} \subset \mathbb R^d$ is a convex compact set and $p$ is an even integer. This is the first algorithm with $\text{poly}(d, \log(1/\epsilon))$ runtime for any fixed $p \ne 2$. Our techniques are based on a computationally efficient version of Sion's theorem for non-compact minmax problems, and extend to more general total search problems that admit low-degree polynomial potentials.

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Constantinos Daskalakis, Gabriele Farina, Brian Hu Zhang. 2026-07-26. Polynomial-time computation of $\ell_p$-contraction fixed points for even $p$. https://arxiv.org/abs/2607.23863

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