Tìm kiếm theo: Tác giả Monique, Laurent

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  • Tác giả : Monique, Laurent; Lucas, Slot;  Người hướng dẫn: -;  Đồng tác giả: - (2022)

    Let S⊆Rn be a compact semialgebraic set and let f be a polynomial nonnegative on S. Schmüdgen’s Positivstellensatz then states that for any η>0, the nonnegativity of f+η on S can be certified by expressing f+η as a conic combination of products of the polynomials that occur in the inequalities defining S, where the coefficients are (globally nonnegative) sum-of-squares polynomials. It does not, however, provide explicit bounds on the degree of the polynomials required for such an expression.