A common variable minimax theorem for graphs

07/30/2021

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by   Ronald R. Coifman, et al.

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7

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Let 𝒢 = {G_1 = (V, E_1), …, G_m = (V, E_m)} be a collection of m graphs defined on a common set of vertices V but with different edge sets E_1, …, E_m. Informally, a function f :V →ℝ is smooth with respect to G_k = (V,E_k) if f(u) ∼ f(v) whenever (u, v) ∈ E_k. We study the problem of understanding whether there exists a nonconstant function that is smooth with respect to all graphs in 𝒢, simultaneously, and how to find it if it exists.