We introduce and study a cone which consists of a class of generalized polynomial functions
and which provides a common framework for recent non-negativity certificates of …

The second-order cone (SOC) is a class of simple convex cones and optimizing over them
can be done more efficiently than with semidefinite programming. It is interesting both in …

Circuit polynomials are polynomials with properties that make it easy to compute sharp and
certifiable global lower bounds for them. Consequently, one may use them to find certifiable …

The arithmetic mean/geometric mean inequality (AM/GM inequality) facilitates classes of
nonnegativity certificates and of relaxation techniques for polynomials and, more generally …

Recently, non-SOS Positivstellens\" atze for polynomials on compact semialgebraic sets,
following the general form of Schm\"{u} dgen's Positivstellensatz, have been derived by …

Circuit polynomials are a certificate of nonnegativity for real polynomials, which can be
derived via a generalization of the classical inequality of arithmetic and geometric means. In …

The cone of sums of nonnegative circuits (SONCs) is a subset of the cone of nonnegative
polynomials/exponential sums, which has been studied extensively in recent years. In this …

Certifying the stability of dynamical systems is a central and challenging task in control
theory and systems analysis. To tackle these problems we present an algorithmic approach …

Electricity is recognized as one of the most pervasive government services. Therefore,
accurate forecasting of electricity demand has a great impact on electricity management. In …

Résumé Cette these étudie le probleme de l'optimisation d'un polynôme trigonométrique
avec symétrie cristallographique. L'optimisation des polynômes trigonométriques était l'objet …