A new bound for Pólya's Theorem with applications to polynomials positive on polyhedra

By Victoria Powers, Bruce Reznick. 2001

213 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/2b57514e84f389967ff71fbf22c5032947b3c794

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization (2000, background): “Some of these e ective bounds are presented in [28, 27, 73].”
Approximation of the Stability Number of a Graph via Copositive Programming (2002, methodology): “2 has recently been given by Powers and Reznik [22].”
Matrix Sum-of-Squares Relaxations for Robust Semi-Definite Programs (2006, methodology): “Similarly as in [27], even if P is not homogenous, it not difficult to derive the following generalization of Handelman’s theorem for the standard simplex and with degree bounds.”
Truncated K-moment problems in several variables (2005, background): “Indeed, recent advances in real algebra make it possible to concretely describe the polynomials nonnegative on certain noncompact semi-algebraic sets ([KuMa], [PoRe1], [ PoRe2 ], [PoSc], [Pre], [Put2], [Sche]), so as to establish moment theorems via the previously intractable Riesz-Haviland approach”
LMI Techniques for Optimization Over Polynomials in Control: A Survey (2010, background): “It is worth mentioning that several bounds on the value of required for achieving necessity in Pólya’s theorem have been found, which however require the knowledge of the minimum of over the simplex, see for instance [31].”
Polynomials that are positive on an interval (2000, background): “The proof of this theorem is contained in the forthcoming paper [19].”
Sums of Squares, Moment Matrices and Optimization Over Polynomials (2009, unknown): “(Pólya [123]; see [125] for a proof).”
Stability of polytopes of matrices via affine parameter-dependent lyapunov functions : Asymptotically exact LMI conditions (2005, background): “Recently, a bound on the value of d , tighter than previous ones from the literature, has been provided in [27].”