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We consider the problem of certifying an inequality of the form f(x) ≥ 0, ∀x ∈ K, where f is a multivariate transcendental function, and K is a compact semialgebraic set. We introduce a certification method, combining semialgebraic optimization and max-plus approximation. We assume that f is given by a syntaxic tree, the constituents of which involve semialgebraic operations as well as some transcendental...
Max-plus based methods have been recently developed to approximate the value function of possibly high dimensional optimal control problems. A critical step of these methods consists in approximating a function by a supremum of a small number of functions (max-plus “basis functions”) taken from a prescribed dictionary. We study several variants of this approximation problem, which we show to be continuous...
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