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Representations of non-negative polynomials having finitely many zeros

Murray Marshall (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

Consider a compact subset $K$ of real $n$ -space defined by polynomial inequalities $g_{1} \geq 0, \dots, g_{s} \geq 0$ . For a polynomial $f$ non-negative on $K$ , natural sufficient conditions are given (in terms of first and second derivatives at the zeros of $f$ in $K$ ) for $f$ to have a presentation of the form $f = t_{0} + t_{1} g_{1} + \dots + t_{s} g_{s}$ , $t_{i}$ a sum of squares of polynomials. The conditions are much less restrictive than the conditions given by Scheiderer in [11, Cor. 2.6]. The proof uses Scheiderer’s main theorem in [11] as well as arguments from quadratic form theory...

Representations of non-negative polynomials via KKT ideals

Dang Tuan Hiep (2011)

Annales Polonici Mathematici

This paper studies the representation of a non-negative polynomial f on a non-compact semi-algebraic set K modulo its KKT (Karush-Kuhn-Tucker) ideal. Under the assumption that f satisfies the boundary Hessian conditions (BHC) at each zero of f in K, we show that f can be represented as a sum of squares (SOS) of real polynomials modulo its KKT ideal if f ≥ 0 on K.

Displaying 41 – 46 of 46

Representations of non-negative polynomials having finitely many zeros

Representations of non-negative polynomials via KKT ideals

Riemann existence theorem and construction of real algebraic curves

Rigid subanalytic sets

Rokhlin conjecture and quotients of complex surfaces by complex conjugation.

Rokhlin's formula for dividing T-curves.

Currently displaying 41 – 46 of 46