4 papers
On the exactness of Lasserre relaxations and pure states over real closed fields
Tom-Lukas Kriel, Markus Schweighofer
Consider a finite system of non-strict polynomial inequalities with solution set . Its Lasserre relaxation of degree is a certain natural linear matrix i…
On the exactness of Lasserre relaxations for compact convex basic closed semialgebraic sets
Markus Schweighofer, Tom-Lukas Kriel
Consider a finite system of non-strict real polynomial inequalities and suppose its solution set is convex, has nonempty interior and is compact. Suppose th…
An introduction to matrix convex sets and free spectrahedra
Tom-Lukas Kriel
The purpose of this paper is to give a self-contained overview of the theory of matrix convex sets and free spectrahedra. We will give new proofs and generalizations of key theorem…
A new proof for the existence of degree bounds for Putinar's Positivstellensatz
Tom-Lukas Kriel
Putinar's Positivstellensatz is a central theorem in real algebraic geometry. It states the following: If you have a set $S= \{ x \in R^n \ | \ g_1 (x) \geq 0, ... , g_m(x) \geq 0\…