Bit-complexity estimates in geometric programming, and application to the polynomial-time computation of the spectral radius of nonnegative tensors - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2023

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

Stéphane Gaubert

Abstract

We show that the spectral radius of nonnegative tensors can be approximated within $\varepsilon$ error in polynomial time. This implies that the maximum of a nonnegative homogeneous $d$-form in the unit ball with respect to $d$-H\"older 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 $\mathbb{R}^n$. Hence, some known upper bounds for the clique number of hypergraphs are polynomially computable.

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hal-04365626 , version 1 (28-12-2023)

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Shmuel Friedland, Stéphane Gaubert. Bit-complexity estimates in geometric programming, and application to the polynomial-time computation of the spectral radius of nonnegative tensors. 2023. ⟨hal-04365626⟩
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