Positive polynomials and sums of squares

By Martyn Marshall. 2008

526 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/ab3d4e80b68b926c35f08190c3206426dcebe4a3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Numerical Analysis

Citations in the corpus

Noncommutative Real Algebraic Geometry Some Basic Concepts and First Ideas (2007, background): “For a noncommutative ∗-algebra A a natural guess is to generalize the latter to c∗ac ∈ ∑A2.”
Optimality conditions and finite convergence of Lasserre’s hierarchy (2012, background): “(Marshall, [16, Theorem 9.5.3] ) Let V = V R ( h ) and f min be the minimum of (1.1).”
Real algebraic geometry (2013, methodology): “This method was pioneered by several researchers including Grigoriev and Vorobjov [46, 45], Renegar [67], Canny [33], Heintz, Roy and Solernò [48], Basu, Pollack and Roy [12] amongst others.”
Positive semidefinite diagonal minus tail forms are sums of squares (2011, background): “Lasserre’s proof uses the ties existing between the theory of moments and sos representations, see [8] or [9].”
Normalizing Flows for Probabilistic Modeling and Inference (2019, background): “Since every positive polynomial of degree 2L can be written as a sum of 2 (or more) squares of polynomials of degree L (Marshall, 2008, Proposition 1.1.2), this fact can be exploited to define a sum-of-squares polynomial transformer (Jaini et al., 2019): τ(zi;hi) = ∫ zi 0 K∑ k=1 ( L∑ `=0 αik` z `…”
Application of the Moment-SOS Approach to Global Optimization of the OPF Problem (2013, background): “In the case of polynomial optimization, one recovers the problem of finding certificates ensuring the positivity of the polynomial on the semi-algebraic set , which involves sums of squares of polynomials [30].”
A generalized flat extension theorem for moment matrices (2009, unknown): “[17] for details).”