Thorsten Theobald's publications
To my homepage
(For copyright reasons, the corresponding preprints do not necessarily agree
with the final publication version.)
To the web page for the textbook on
Real Algebraic Geometry and Optimization
Recent articles:
- Nonnegativity of signomials with Newton simplex over convex sets
With J. Ellwanger and T. de Wolff.
- A stable-set bound and maximal numbers of Nash equilibria in bimatrix games
With C. Ickstadt, B. von Stengel.
Repository for the data of the stable-set computations
- Semidefinite network games: multiplayer minimax and complementarity problems
With C. Ickstadt, E. Tsigaridas and A. Varvitsiotis.
- Symmetric SAGE and SONC forms, exactness and quantitative gaps
With P. Moustrou, C. Riener and H. Verdure.
J. Symbolic Computation, 127:102374, 2025. Special issue in memory and
honor of Agnes Szanto.
- Semidefinite games
With C. Ickstadt and E. Tsigaridas.
Internat. J. Game Theory 53:827-857, 2024.
Link to online published version here
- Relative entropy methods in constrained polynomial
and signomial optimization
In M. Kočvara, B. Mourrain and C. Riener (eds.):
Polynomial Optimization, Moments, and Applications,
Springer, 23-51, 2023.
- Combinatorics and preservation
of conically stable polynomials
With G. Codenotti and S. Gardoll.
J. Algebraic Combinatorics 58, 811-836, 2023.
- Imaginary projections:
complex versus real coefficients
With S. Gardoll and M. Sayyary Namin.
J. Pure and Applied Algebra, 227(6):107308, 2023.
- Sublinear
circuits and the constrained signomial nonnegativity problem
With R. Murray and H. Naumann.
Math. Programming 198:471-505, 2023.
Link to online published version here
- Symmetry reduction for
AM/GM-based optimization
With P. Moustrou, H. Naumann, C. Riener, H. Verdure.
SIAM J. Optimization 32:765-785, 2022.
- Sublinear circuits for
polyhedral sets
With H. Naumann.
Vietnam J. Math. 50:447-468, 2022, special issue on the honor of
Bernd Sturmfels.
(Link to online published version here)
- Special issue edited, with A. Bernardi and C. D'Andrea:
J. Symbolic Computation Special Issue of MEGA 2019.
Foreword (including the overview on the papers -
link to online published
version):
vol. 109:199-201, 2022.
Preprint version
on HAL
- Conic stability of polynomials and positive maps
With P. Dey and S. Gardoll.
J. Pure and Applied Algebra (special issue of the Arctic
Applied Algebra Conference) 225(7):106610, 2021.
- A unified framework of SONC and SAGE polynomials and its duality theory
With L. Katthän and H. Naumann.
Math. of Computation 90:1297-1322, 2021.
- The S-cone and a primal-dual view on second-order representability
With H. Naumann.
Beiträge zur Algebra und Geometrie 62:229-249, 2021 (special issue on
the 50th anniversary of the journal).
(Link to online published version here)
- The dual cone of sums of nonnegative circuit polynomials
With M. Dressler and H. Naumann.
Advances in Geometry 21:227-236, 2021.
- Block-sparse recovery of semidefinite systems and generalized null space conditions
With J. Heuer, F. Matter and M. E. Pfetsch.
Linear Algebra and its Applications 603:479-495, 2020.
(Link to online published version here)
- Irreducible infeasible subsystems of semidefinite systems
With K. Kellner and M. E. Pfetsch.
J. Optimization Theory and Applications 181:727-742, 2019.
(Link to online published version here)
- Imaginary projections of polynomials
With T. Jörgens and T. de Wolff.
Journal of Symbolic Computation 91:181-199, 2019 (special issue of
MEGA 2017).
- Conic stability of polynomials
With T. Jörgens.
Research in the Mathematical Sciences 5:26, 2018.
- Hyperbolicity cones and imaginary projections
With T. Jörgens.
Proceedings of the American Mathematical Society 146:4105-4116, 2018.
- Some recent developments in spectrahedral computation
In Algorithmic and Experimental Methods in Algebra, Geometry,
and Number Theory
(G. Böckle, W. Decker, G. Malle, eds.),
717-739, Springer, 2017.
- Mixed Ehrhart polynomials
With C. Haase, M. Juhnke-Kubitzke, R. Sanyal.
Electron. J. Comb. 24:P1.10, 2017.
- Norms of roots of trinomials
With T. de Wolff.
Math. Annalen 366:219-247, 2016.
- Sum of squares certificates for containment of H-polytopes in V-polytopes
With K. Kellner.
SIAM J. Discrete Math. 30:763-776, 2016.
- A semidefinite hierarchy
for containment of spectrahedra
With K. Kellner and C. Trabandt.
SIAM J. Optimization 25:1013-1033, 2015.
- Approximating amoebas and
coamoebas by sums of squares
With T. de Wolff.
Math. of Computation 84:455--473, 2015.
- Containment problems for
polytopes and spectrahedra
With K. Kellner and C. Trabandt.
SIAM J. Optimization 23:1000-1020, 2013.
- Amoebas of genus at most one
With T. de Wolff.
Advances in Mathematics 239:190--213, 2013.
- Exploiting symmetries in
SDP-relaxations for polynomial optimization
With C. Riener, L. Jansson Andrén and J.B. Lasserre.
Math. of Operations Research 38:122-141, 2013.
- Determining a rotation of a tetrahedron
from a projection
With R.J. Gardner and P. Gronchi.
Discrete and Computational Geometry 48:749-765, 2012.
- Projections of tropical varieties and
their self-intersections
With K. Hept.
Advances in Geometry 12:203-228, 2012.
- Combinatorics and genus
of tropical intersections and Ehrhart theory
With R. Steffens.
SIAM J. Discrete Math. 24:17-32, 2010.
- Games of fixed rank:
A hierarchy of bimatrix games
With R. Kannan.
Econom. Theory 42:157-173, 2010.
- Mixed volume techniques for
embeddings of Laman graphs
With R. Steffens.
Computational Geometry: Theory and Applications 43:84-93, 2010.
- Tropical bases by
regular projections
With K. Hept.
Proceedings of the American Mathematical Society 137:2233-2241, 2009
- Enumerating the
Nash equilibria of rank 1-games
In D. Avis, D. Bremner, A. Deza (eds.): Polyhedral Computation.
AMS/CRM, 115-130, 2009.
- Algorithmische Geometrie: Polyedrische und algebraische Methoden
With M. Joswig.
Vieweg-Verlag, 2008 (in German). Vorwort, Inhaltsverzeichnis und Übersicht.
- Line problems in
nonlinear computational geometry
With F. Sottile.
Surveys on Discrete and Computational Geometry: Twenty years later.
Contemporary Mathematics, vol. 453, 411-432, AMS, 2008.
- Games of fixed rank:
A hierarchy of bimatrix games
With R. Kannan.
Proc. Symposium on Discrete Algorithms (SODA 2007), New Orleans (LA),
1124-1132, 2007.
- Positive Polynome und semidefinite
Optimierung (in German)
With C. Riener.
Jahresbericht der Deutschen Mathematiker-Vereinigung 110:57-74, 2007.
- On the frontiers of polynomial
computations in tropical geometry
Journal of Symbolic Computation 41:1360-1375, 2006.
- Radii minimal projections of polytopes and
constrained optimization of symmetric polynomials
With R. Brandenberg.
Advances in Geometry 6:71-83, 2006.
- Geometrie und Kombinatorik von
Nash-Gleichgewichten (in German)
Mathematische Semesterberichte 52:221-239, 2005.
-
On the complexity of visibility problems with moving
viewpoints
With P. Gritzmann.
Combinatorial and Computational Geometry, MSRI publications,
vol. 52, 377-397,
Cambridge University Press, 2005.
- First steps in tropical geometry
With J. Richter-Gebert and B. Sturmfels.
In G.L. Litvinov, V.P. Maslov (eds.): Idempotent Mathematics and Mathematical
Physics, Contemporary Mathematics, vol. 377, 289-317, AMS, 2005.
-
Real k-flats tangent to quadrics in R^n
With F. Sottile.
Proceedings of the American
Mathematical Society 133:2835-2844, 2005.
- Exact analysis of optimal configurations in radii computations
With R. Brandenberg.
European Workshop on Computational Geometry (Eindhoven),
135-138, 2005.
- Radii of simplices and some applications to geometric inequalities
With R. Brandenberg.
Beiträge zur Algebra und Geometrie 45:581-594, 2004.
-
Algebraic methods for computing smallest enclosing and circumscribing
cylinders of simplices
With R. Brandenberg.
Applicable Algebra in Engineering, Communication
and Computing 14:439-460, 2004.
-
Common transversals and tangents to two lines and two quadrics in P^3
With G. Megyesi and F. Sottile.
Discrete and Computational Geometry
30:543-571, 2003.
Accompanying Web page
- Visibility computations: From discrete algorithms to real algebraic geometry
In S. Basu and L. Gonzalez-Vega (eds.), Algorithmic and Quantitative Real Algebraic Geometry, AMS DIMACS series, vol. 60, 207-219, 2003
-
Homotopy methods for real-time visualization of geometric tangent problems
With D. Kotzor.
Video presentation, ACM Symposium on Computational Geometry 2002 (Barcelona).
Accompanying article in the proceedings, pp. 275-276
-
Lines tangent to 2n-2 spheres in R^n
With F. Sottile.
Accompanying Web page
Transactions of the AMS 354(12):4815-4829, 2002
-
Computing amoebas
Experimental Mathematics 11:513-526, 2002
-
An enumerative geometry framework for algorithmic line problems in R^3
SIAM Journal on Computing 31(4), pp. 1212-1228, 2002
-
How to realize a given number of tangents to four unit balls in R^3
Mathematika 48:51-62, 2001
-
Common tangents to four unit balls in R^3
With I.G. Macdonald and J. Pach.
Discrete and Computational Geometry 26(1), pp. 1-17, 2001
Some former work (list not complete):
- Local encoding transformations for optimizing OBDD-representations
of finite state machines.
With Ch. Meinel.
Formal Methods in System Design 18, pp. 285-301 (2001)
- Linear sifting of decision diagrams and its application in synthesis
IEEE Transactions on Computer-Aided Design 19(5), pp. 521-533 (2000)
- Ordered binary decision diagrams and their significance in computer-aided
design of VLSI circuits.
With Ch. Meinel.
Journal of Circuits, Systems, and Computers 9(3 & 4), pp. 181-198 (1999)
- On the influence of the state encoding on OBDD-representations of finite
state machines.
With Ch. Meinel.
Theoretical Informatics and Applications 33(1), pp. 21-31 (1999)
- How to break Shamir's asymmetric basis.
In Advances in Cryptology: Proceedings of CRYPTO '95 (Santa Barbara)
Springer Lecture Notes in Computer Science, Vol. 963, pp. 136-147 (1995)
Habilitation thesis:
Books:
Einführung in die computerorientierte Mathematik mit Sage. (In German.)
With S. Iliman.
Springer Spektrum, appeared 10/2015
Homepage of the book
Web page at Springer
Textbook Polyhedral and Algebraic Methods in Computational Geometry.
With M. Joswig.
Springer, Universitext, 2013. See Web page at Springer.
Earlier German version: Algorithmische Geometrie. Polyedrische und Algebraische Methoden. Vieweg, 2008.
See Web page at Springer.
Book edited: Nonlinear Computational Geometry, IMA Volume, Springer, 2009.
With I. Emiris and F. Sottile.
See Web page at Springer.
Algorithms and Data Structures in VLSI Design: OBDD - Foundations and Applications.
With Ch. Meinel.
Springer, 1998.
Complete pdf version
German version: Algorithmen und Datenstrukturen im VLSI-Design, Springer, 1998.
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