Thorsten Theobald's publications

To the web page for the textbook on Real Algebraic Geometry and Optimization

Recent articles:

• Symmetric SAGE and SONC forms, exactness and quantitative gaps
  With P. Moustrou, C. Riener and H. Verdure.

• Semidefinite network games: multiplayer minimax and complementarity problems
  With C. Ickstadt, E. Tsigaridas and A. Varvitsiotis.

• Relative entropy methods in constrained polynomial and signomial optimization
  In M. Kočvara, B. Mourrain and C. Riener (eds.): Polynomial Optimization, Moments, and Applications, Springer, 2023.

• Semidefinite games
  With C. Ickstadt and E. Tsigaridas.

• 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:

• New Algebraic Methods in Computational Geometry. TU München, 2003.

Books:

Earlier German version: Algorithmische Geometrie. Polyedrische und Algebraische Methoden. Vieweg, 2008.
See Web page at Springer.

German version: Algorithmen und Datenstrukturen im VLSI-Design, Springer, 1998.

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