Research Focus Real Geometry and Algebra > Markus Schweighofer

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Markus Schweighofer - Publications

Preprints:

Spectrahedral relaxations of hyperbolicity cones
62 pages
^{arxiv.org/abs/1907.13611}

Published articles:

Thorsten Theobald: "Real Algebraic Geometry and Optimization" (Book Review)
Jahresbericht der Deutschen Mathematiker-Vereinigung 126, 313-321 (2024)
^{doi:10.1365/s13291-024-00288-0}
with Luis Felipe Vargas
Sum-of-squares certificates for copositivity via test states
SIAM Journal on Applied Algebra and Geometry 8, No. 4, 797-820 (2024)
^{arxiv.org/abs/2310.12853} ^{doi:10.1137/23M1611798}
with David Sawall
Amalgamation of real zero polynomials
Indagationes Mathematicae 35, 37-59 (2024)
^{doi:10.1016/j.indag.2023.08.002}
with Victor Magron, Mohab Safey El Din and Trung Hieu Vu
Exact SOHS decompositions of trigonometric univariate polynomials with Gaussian coefficients
ISSAC '22, Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation, 325-332 (2022)
^{doi:10.1145/3476446.3535480}
with Grigoriy Blekherman, Mario Kummer, Cordian Riener and Cynthia Vinzant
Generalized eigenvalue methods for Gaussian quadrature rules
Annales Henri Lebesgue 3, 1327-1341 (2020)
^{doi:10.5802/ahl.62}
with Tom-Lukas Kriel
On the exactness of Lasserre relaxations and pure states over real closed fields
Foundations of Computational Mathematics 19, 1223-1263 (2019)
^{doi:10.1007/s10208-018-9406-z}
with Victor Magron and Mohab Safey El Din
Algorithms for weighted sums of squares decomposition of non-negative univariate polynomials
Journal of Symbolic Computation 93, 200-220 (2019)
^{doi:10.1016/j.jsc.2018.06.005}
This article comes with a Maple library.
with Bill Helton, Igor Klep and Scott McCullough
Dilations, linear matrix inequalities, the matrix cube problem and beta distributions
104 pages
Memoirs of the American Mathematical Society 257, Number 1232 (2019)
with Tom-Lukas Kriel
On the exactness of Lasserre relaxations for compact convex basic closed semialgebraic sets
SIAM Journal on Optimization 28, No. 2, 1796-1816 (2018)
^{doi:10.1137/17M1128290}
with Cordian Riener
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
Journal of Complexity 45, 22-54 (2018)
^{doi:10.1016/j.jco.2017.10.002}
with Sabine Burgdorf, Ken Dykema and Igor Klep
Addendum to "Connes' embedding conjecture and sums of hermitian squares"
Advances in Mathematics 252, 805-811 (2014)
^{doi:10.1016/j.aim.2013.10.020}
with Igor Klep
An exact duality theory for semidefinite programming based on sums of squares
Mathematics of Operations Research 38, 569-590 (2013)
^{doi:10.1287/moor.1120.0584}
see also the Oberwolfach Preprint with the erratum fixing a minor problem.
with Sabine Burgdorf and Claus Scheiderer
Pure states, nonnegative polynomials and sums of squares
Commentarii Mathematici Helvetici 87, Issue 1, 113-140 (2012)
^{doi:10.4171/CMH/250}
with Igor Klep
Pure states, positive matrix polynomials and sums of hermitian squares
Indiana University Mathematics Journal 59, No. 3, 857-874 (2010)
^{doi:10.1512/iumj.2010.59.4107}
with Tim Netzer and Daniel Plaumann
Exposed faces of semidefinitely representable sets
SIAM Journal on Optimization 20, No. 4, 1944-1955 (2010)
^{doi:10.1137/090750196}
with Igor Klep
Sums of hermitian squares and the BMV conjecture
Journal of Statistical Physics 133, No. 4, 739-760 (2008)
^{doi:10.1007/s10955-008-9632-x}
This article comes with a Mathematica file.
with Igor Klep
Connes' embedding conjecture and sums of hermitian squares
Advances in Mathematics 217, No. 4, 1816-1837 (2008)
^{doi:10.1016/j.aim.2007.09.016}
There is a serious problem which is fixed here.
with David Grimm and Tim Netzer
A note on the representation of positive polynomials with structured sparsity
Archiv der Mathematik 89, No. 5, 399-403 (2007)
^{doi:10.1007/s00013-007-2234-z}
with Igor Klep
A Nichtnegativstellensatz for polynomials in noncommuting variables
Israel Journal of Mathematics 161, No. 1, 17-27 (2007)
^{doi:10.1007/s11856-007-0070-2}
with Jiawang Nie
On the complexity of Putinar's Positivstellensatz
Journal of Complexity 23, No. 1, 135-150 (2007)
^{doi:10.1016/j.jco.2006.07.002}
Global optimization of polynomials using gradient tentacles and sums of squares
SIAM Journal on Optimization 17, No. 3, 920-942 (2006)
^{doi:10.1137/050647098}
Certificates for nonnegativity of polynomials with zeros on compact semialgebraic sets
Manuscripta Mathematica 117, No. 4, 407-428 (2005)
^{doi:10.1007/s00229-005-0568-z}
Optimization of polynomials on compact semialgebraic sets
SIAM Journal on Optimization 15, No. 3, 805-825 (2005)
^{doi:10.1137/s1052623403431779}
On the complexity of Schmüdgen's Positivstellensatz
Journal of Complexity 20, No. 4, 529-543 (2004)
doi:10.1016/j.jco.2004.01.005
Iterated rings of bounded elements and generalizations of Schmüdgen's Positivstellensatz
Journal für die reine und angewandte Mathematik 554, 19-45 (2003)
^{http://www.degruyter.de/journals/crelle/2003/554_19.html}
There is an erratum fixing a minor problem.
An algorithmic approach to Schmüdgen's Positivstellensatz
Journal of Pure and Applied Algebra 166, 307-319 (2002)
^{doi:10.1016/S0022-4049(01)00041-X}

Thesis:

Iterated rings of bounded elements and generalizations of Schmüdgen's theorem
Dissertation an der Universität Konstanz (2002)
There is an erratum fixing a minor problem.

Diplomarbeit:

Algorithmische Beweise für Nichtnegativ- und Positivstellensätze
Diplomarbeit an der Universität Passau (1999)