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Sum-of-squares hierarchies for binary polynomial optimization
[article]
2022
arXiv
pre-print
We consider the sum-of-squares hierarchy of approximations for the problem of minimizing a polynomial f over the boolean hypercube 𝔹^n={0,1}^n. This hierarchy provides for each integer r ∈ℕ a lower bound f_(r) on the minimum f_min of f, given by the largest scalar λ for which the polynomial f - λ is a sum-of-squares on 𝔹^n with degree at most 2r. We analyze the quality of these bounds by estimating the worst-case error f_min - f_(r) in terms of the least roots of the Krawtchouk polynomials. As
arXiv:2011.04027v3
fatcat:io3h2ofz2bdktkh4ct3ma7ufqe