A Spectral Generalization of Von Neumann Minimax Theorem

Bahman Kalantari

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arXiv · 1905.09762

A Spectral Generalization of Von Neumann Minimax Theorem

Bahman Kalantari

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Abstract

Given $n \times n$ real symmetric matrices $A_1, \dots, A_m$, the following {\it spectral minimax} property holds: $$\min_{X \in \mathbfΔ_n} \max_{y \in S_m} \sum_{i=1}^m y_iA_i \bullet X=\max_{y \in S_m} \min_{X \in \mathbfΔ_n} \sum_{i=1}^m y_iA_i \bullet X,$$ where $S_m$ is the simplex and $\mathbfΔ_n$ the spectraplex. For diagonal $A_i$'s this reduces to the classic minimax.

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Bahman Kalantari. 2019-05-23. A Spectral Generalization of Von Neumann Minimax Theorem. https://arxiv.org/abs/1905.09762

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