Computing the global optimum of a multivariate polynomial over the reals

Abstract

Let f be a polynomial in Q[X<sub>1</sub>, ..., X<sub>n</sub>] of degree D. We provide an efficient algorithm in practice to compute the global supremum sup<sub>x∈ R<sup>n</sup></sub> f(x) of f (or its infimum inf<sub>{x∈ R<sup>n</sup>}</sub>f(x)). The complexity of our method is bounded by D<sup>O</sup>(n)}. In a probabilistic model, a more precise result… (More)
DOI: 10.1145/1390768.1390781

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