Graduate Texts in Mathematics bridge the gap between passive study and creative
understanding, offering graduate-level introductions to advanced topics in mathematics. The …

Page 1 LNCIS 390 LECTURE NOTES IN CONTROL AND INFORMATION SCIENCES Graziano
Chesi Andrea Garulli Alberto Tesi Antonio Vicino Homogeneous Polynomial Forms for …

This paper gives a survey, with detailed references to the literature, on recent developments
in real algebra and geometry concerning the polarity between positivity and sums of …

In the smallest cases where there exist nonnegative polynomials that are not sums of
squares we present a complete explanation of this distinction. The fundamental reason that …

Our first contribution in this paper is to prove that three natural sum of squares (sos) based
sufficient conditions for convexity of polynomials, via the definition of convexity, its first order …

If a real polynomial f can be written as a sum of squares of real polynomials, then clearly f is
nonnegative on Rn, and an explicit expression of f as a sum of squares is a certificate of …

Polynomial optimization encompasses a very rich class of problems in which both the
objective and constraints can be written in terms of polynomials on the decision variables …

The book gives a contemporary account of the study of the class of projective algebraic
surfaces known as Enriques surfaces. These surfaces were discovered more than 125 years …

We employ positivity of Riesz functionals to establish representing measures (or
approximate representing measures) for truncated multivariate moment sequences. For a …

We study the geometry underlying the difference between non-negative polynomials and
sums of squares (SOS). The hypersurfaces that discriminate these two cones for ternary …