This tutorial is about new system analysis techniques that were developed in the past few
years based on the sum of squares decomposition. We present stability and robust stability …

Matrix theory is one of the most fundamental tools of mathematics and science, and a
number of classical books on matrix analysis have been written to explore this theory. As a …

We consider the problem of generating motion plans for a robot that are guaranteed to
succeed despite uncertainty in the environment, parametric model uncertainty, and …

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 …

Many important applications in global optimization, algebra, probability and statistics,
applied mathematics, control theory, financial mathematics, inverse problems, etc. can be …

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 …

Serving both as an introduction to the subject and as a reference, this book presents the
theory in elegant form and with modern concepts and notation. It covers the general theory …

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 …