The Complexity of Min-Max Optimization for Quadratic Polynomials

Martino Bernasconi; Matteo Castiglioni; Andrea Celli; Alexandros Hollender

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arXiv · 2606.17000

The Complexity of Min-Max Optimization for Quadratic Polynomials

Martino Bernasconi·Matteo Castiglioni·Andrea Celli·Alexandros Hollender

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Abstract

We prove that computing approximate stationary points of min-max optimization over the hypercube is PPAD-hard for quadratic polynomials. This holds even when the polynomials are multilinear, each variable appears in at most three monomials, and the approximation factor is inverse polynomial. As a direct consequence, we obtain the first PPAD-hardness results for two-team zero-sum polymatrix games.

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Martino Bernasconi, Matteo Castiglioni, Andrea Celli, Alexandros Hollender. 2026-06-15. The Complexity of Min-Max Optimization for Quadratic Polynomials. https://arxiv.org/abs/2606.17000

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