Chordal and factor-width decomposition methods for semidefinite programming and
polynomial optimization have recently enabled the analysis and control of large-scale linear …

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

This is the first comprehensive introduction to the powerful moment approach for solving
global optimization problems (and some related problems) described by polynomials (and …

In recent years, optimization theory has been greatly impacted by the advent of sum of
squares (SOS) optimization. The reliance of this technique on large-scale semidefinite …

In the first part of this thesis, we introduce a specific class of Linear Matrix Inequalities (LMI)
whose optimal solution can be characterized exactly. This family corresponds to the case …

A hierarchy of convex relaxations for semialgebraic problems is introduced. For questions
reducible to a finite number of polynomial equalities and inequalities, it is shown how to …

Convexity is a simple idea that manifests itself in a surprising variety of places. This fertile
field has an immensely rich structure and numerous applications. Barvinok demonstrates …

In this chapter we begin the study of the multidimensional moment problem. The passage to
dimensions d≥ 2 brings new difficulties and unexpected phenomena. In Sect. 3.2 we …

Hilbert's 17th Problem asks whether a real positive semidefinite polynomial can be
expressed as a sum of squares of rational functions. Artin answered “yes” in the 1920's …

A few words on the second edition. By a nice coincidence, Springer's proposal to revise the
book came when I was giving a serious thought to the idea. Ten years have passed and my …