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We consider the problem of certifying lower bounds for real-valued multivariate transcendental functions. The functions we are dealing with are nonlinear and involve semialgebraic operations as well as some transcendental functions like $$\cos ,\,\arctan ,\,\exp $$ cos , arctan , exp , etc. Our general framework is to use different approximation methods to relax the original problem into...
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...
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