Bit-complexity estimates in geometric programming, and application to the polynomial-time computation of the spectral radius of nonnegative tensors

01/25/2023

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by   Shmuel Friedland, et al.

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We show that the spectral radius of nonnegative tensors can be approximated within ε error in polynomial time. This implies that the maximum of a nonnegative homogeneous d-form in the unit ball with respect to d-Hölder norm can be approximated in polynomial time. These results are deduced by establishing bit-size estimates for the near-minimizers of functions given by suprema of finitely many log-Laplace transforms of discrete nonnegative measures on ℝ^n. Hence, some known upper bounds for the clique number of hypergraphs are polynomially computable.