Richard Leroy

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In this article, we address the question of minimizing a real polynomial over the standard simplex. This problem can be solved with a branch-andbound method, using the Bernstein form of the polynomial. Such methods have been widely studied from a numerical point of view, and refinements have been proposed to speed up the computational time. We are here(More)
We consider the problem of bounding away from 0 the minimum value m taken by a polynomial P ∈ Z [X1, . . . , Xk] over the standard simplex ∆ ⊂ R, assuming that m > 0. Recent algorithmic developments in real algebraic geometry enable us to obtain a positive lower bound on m in terms of the dimension k, the degree d and the bitsize τ of the coefficients of P(More)
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