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

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 …

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 …

This paper is concerned with polynomial optimization problems. We show how to exploit
term (or monomial) sparsity of the input polynomials to obtain a new converging hierarchy of …

Numerous tasks in control systems involve optimization problems over polynomials, and
unfortunately these problems are in general nonconvex. In order to cope with this difficulty …

This paper addresses the state feedback control synthesis problems for nonlinear systems,
either without or with guaranteed cost or H/sub/spl infin//performance objectives. By …

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 …

Unconstrained and inequality constrained sparse polynomial optimization problems (POPs)
are considered. A correlative sparsity pattern graph is defined to find a certain sparse …

Checking non-negativity of polynomials using sum-of-squares has recently been
popularized and found many applications in control. Although the method is based on …