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 …

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

We consider the problem of minimizing a polynomial over a semialgebraic set defined by
polynomial equations and inequalities, which is NP-hard in general. Hierarchies of …

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 …

Copositive linear Lyapunov functions are used along with dissipativity theory for stability
analysis and control of uncertain linear positive systems. Unlike usual results on linear …

The study of positive polynomials brings together algebra, geometry and analysis. The
subject is of fundamental importance in real algebraic geometry when studying the …

Sherali and Adams (1990), Lovász and Schrijver (1991) and, recently, Lasserre (2001b)
have constructed hierarchies of successive linear or semidefinite relaxations of a 0–1 …

We compare algorithms for global optimization of polynomial functions in many variables. It
is demonstrated that existing algebraic methods (Gr\" obner bases, resultants, homotopy …

Moment and polynomial optimization has received high attention in recent decades. It has
beautiful theory and efficient methods, as well as broad applications for various …