On the complexity of Schmu"dgen's Positivstellensatz. - Markus Schweighofer (J. Complex., 2004)

Optimization of Polynomials on Compact Semialgebraic Sets. - Markus Schweighofer (SIAM J. Optim., 2005)

Global Optimization of Polynomials Using Gradient Tentacles and Sums of Squares. - Markus Schweighofer (SIAM J. Optim., 2006)

On the complexity of Putinar's Positivstellensatz. - Jiawang Nie; Markus Schweighofer (J. Complex., 2007)

Describing convex semialgebraic sets by linear matrix inequalities. - Markus Schweighofer (ISSAC, 2009)

Exposed Faces of Semidefinitely Representable Sets. - Tim Netzer; Daniel Plaumann; Markus Schweighofer (SIAM J. Optim., 2010)

An Exact Duality Theory for Semidefinite Programming Based on Sums of Squares. - Igor Klep; Markus Schweighofer (Math. Oper. Res., 2013)

Algorithms for Weighted Sums of Squares Decomposition of Non-negative Univariate Polynomials. - Victor Magron; Mohab Safey El Din; Markus Schweighofer (CoRR, 2017)

Optimization approaches to quadrature: New characterizations of Gaussian quadrature on the line and quadrature with few nodes on plane algebraic curves, on the plane and in higher dimensions. - Cordian Riener; Markus Schweighofer (J. Complex., 2018)

On the Exactness of Lasserre Relaxations for Compact Convex Basic Closed Semialgebraic Sets. - Tom-Lukas Kriel; Markus Schweighofer (SIAM J. Optim., 2018)

On the Exactness of Lasserre Relaxations and Pure States Over Real Closed Fields. - Tom-Lukas Kriel; Markus Schweighofer (Found. Comput. Math., 2019)

Algorithms for weighted sum of squares decomposition of non-negative univariate polynomials. - Victor Magron; Mohab Safey El Din; Markus Schweighofer (J. Symb. Comput., 2019)

Exact SOHS Decompositions of Trigonometric Univariate Polynomials with Gaussian Coefficients. - Victor Magron; Mohab Safey El Din; Markus Schweighofer; Trung Hieu Vu (ISSAC, 2022)

Sum-of-Squares Certificates for Copositivity via Test States. - Markus Schweighofer; Luis Felipe Vargas (SIAM J. Appl. Algebra Geom., 2024)