116 citations · 258 across the 22 of their papers we have counts for
6 papers · 1 filter
Amalgamation of real zero polynomials
David Sawall, Markus Schweighofer
With this article, we hope to launch the investigation of what we call the real zero amalgamation problem. Whenever a polynomial arises from another polynomial by substituting zero…
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…
On the complexity of Putinar's Positivstellensatz
Jiawang Nie, Markus Schweighofer
We prove an upper bound on the degree complexity of Putinar's Positivstellensatz. This bound is much worse than the one obtained previously for Schmüdgen's Positivstellensatz but i…
Global optimization of polynomials using gradient tentacles and sums of squares
Markus Schweighofer
In this work, the combine the theory of generalized critical values with the theory of iterated rings of bounded elements (real holomorphy rings). We consider the problem of comput…
On the complexity of Putinar's Positivstellensatz
Jiawang Nie, Markus Schweighofer
This paper has been withdrawn by the author due to its publication