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

For a non-empty, finite subset A⊆ N 0 n let C sonc (𝒜)∈ ℝ [x 1,..., xn] be the cone of sums of
non-negative circuit polynomials with support 𝒜. We derive a representation of the dual cone …

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 …

Abstract Conditional Sums-of-AM/GM-Exponentials (conditional SAGE) is a decomposition
method to prove nonnegativity of a signomial or polynomial over some subset X of real …

This book provides a comprehensive and user-friendly exploration of the tremendous recent
developments that reveal the connections between real algebraic geometry and …

The S S-cone provides a common framework for cones of polynomials or exponential sums
which establish non-negativity upon the arithmetic-geometric inequality, in particular for …

In this article, we combine sums of squares (SOS) and sums of nonnegative circuit (SONC)
forms, two independent nonnegativity certificates for real homogeneous polynomials. We …

Although the specific structures of electricity markets are diverse around the world, they were
all conceived on the premise of predictable, controllable generation with nonnegligible …

Relative entropy programs belong to the class of convex optimization problems. Within
techniques based on the arithmetic-geometric mean inequality, they facilitate to compute …