Publications

• C. Helmberg, A. Pichler.
  Dynamic Scaling and Submodel Selection in Bundle Methods for Convex Optimization,
  Preprint 2017-04, Technische Universität Chemnitz, Fakultät für Mathematik, August 2017.
   
• C. Helmberg, U. Schwerdtfeger, I. Rocha.
  A Combinatorial Algorithm for Minimizing the Maximum Laplacian Eigenvalue of Weighted Bipartite Graphs,
  SIAM J. Discrete Math., Vol. 31, No. 2, pp. 1196–1216, 2017.
  (Preprint 2015-12, Technische Universität Chemnitz, Fakultät für Mathematik, July 2015.)
   
• C. Helmberg, V. Trevisan.
  Spectral threshold dominance, Brouwer's Conjecture and maximality of Laplacian energy,
  Linear Algebra and its Applications, Volume 512, 1 January 2017, Pages 18-31.
  (Preprint 2015-08, Technische Universität Chemnitz, Fakultät für Mathematik, June 2015)
   
• C. Helmberg, V. Trevisan.
  Threshold Graphs of Maximal Laplacian Energy
  Discrete Mathematics, Vol. 338 (7), 1075 - 1084, July 2015.
  (Preprint 2014-02, Technische Universität Chemnitz, Fakultät für Mathematik, January 2014).
   
• C. Helmberg, S. Richter, D. Schupke.
  A Chance Constraint Model for Multi-Failure Resilience in Communication Networks,
  Preprint 2015-09, Technische Universität Chemnitz, Fakultät für Mathematik, June 2015.
   
• C. Helmberg, M. L. Overton, and F. Rendl.
  The Spectral Bundle Method with Second-Order Information
  Optimization Methods and Software, Volume 29, Issue 4, July 2014, pages 855-876 (DOI: 10.1080/10556788.2013.858155)
  (Preprint 2012-10, Technische Universität Chemnitz, Fakultät für Mathematik, September 2012.)
• F. Fischer, C. Helmberg.
  A Parallel Bundle Framework for Asynchronous Subspace Optimisation of Nonsmooth Convex Functions
  SIAM J. Optim, Vol. 24, No. 2, pp. 795-822, 2014.
  (Preprint 2013-08, Technische Universität Chemnitz, Fakultät für Mathematik, July 2013)
• F. Fischer, C. Helmberg.
  Dynamic Graph Generation for the Shortest Path Problem in Time Expanded Networks
  Mathematical Programming A, Volume 143, Issue 1-2, pp 257-297, February 2014, DOI: 10.1007/s10107-012-0610-3
  (Preprint 2011-10: Dynamic Graph Generation for Large Scale Operational Train Timetabling
  Technische Universität Chemnitz, Fakultät für Mathematik, July 2011.)
• A. Fischer, C. Helmberg.
  The Symmetric Quadratic Traveling Salesman Problem
  Mathematical Programming A, Volume 142, Issue 1-2, pp 205-254, December 2013, DOI: 10.1007/s10107-012-0568-1
  (Preprint 2011-08, Technische Universität Chemnitz, Fakultät für Mathematik, April 2011.)
• F. Göring, C. Helmberg, and S. Reiss.
  On Minimizing the Spectral Width of Graph Laplacians and Associated Graph Realizations
  SIAM J. Optim. (2013), Vol. 23, No. 2, pp. 834-856, DOI: 10.1137/110859658.
  (Preprint 2011-04, Technische Universität Chemnitz, Fakultät für Mathematik, Februar 2011)
• M. Armbruster, M. Fügenschuh, C. Helmberg, and A. Martin.
  LP and SDP Branch-and-Cut Algorithms for the Minimum Graph Bisection Problem: A Computational Comparison
  Mathematical Programming C, 4(3) 2012, 275-306, DOI: 10.1007/s12532-012-0040-5
  (Preprint 2011-6, Technische Universität Chemnitz, Fakultät für Mathematik, March 2011.
  
• F. Fischer and C. Helmberg.
  Dynamic Graph Generation and Dynamic Rolling Horizon Techniques in Large Scale Train Timetabling
  Proceedings of the 10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems, T. Erlebach and M. Lübbecke (Eds.), OpenAccess Series in Informatics (OASIcs) 14, Schloss Dagstuhl--Leibniz-Zentrum für Informatik, Germany, Sep. 2010, pp. 45--60.
• C. Helmberg and S. Reiss.
  A note on Fiedler vectors interpreted as graph realizations
  Operations Research Letters, Volume 38, Issue 4, July 2010, Pages 320-321.
  (Preprint 2010-1, Technische Universität Chemnitz, Fakultät für Mathematik, Jan 2010.)
  
• C. Helmberg.
  Network Models with Convex Cost Structure like Bundle Methods
  Proceedings of Dagstuhl Seminar 09261 - Models and Algorithms for Optimization in Logistics, 2009.
• F. Göring, C. Helmberg, and S. Reiss.
  Graph Realizations Associated with Minimizing the Maximum Eigenvalue of the Laplacian
  Mathematical Programming A, 131(1-2) 2012, 95 - 111. DOI: 10.1007/s10107-010-0344-z
  (Preprint 2009-10, Technische Universität Chemnitz, Fakultät für Mathematik, May 2009.)
• F. Göring, C. Helmberg, and M. Wappler.
  The Rotational Dimension of a Graph
  Journal of Graph Theory, Volume 66, Issue 4, April 2011, pp. 283-302.
  (Preprint 2008-16, Technische Universität Chemnitz, Fakultät für Mathematik, October 2008.)
  
• F. Fischer, C. Helmberg, J. Janßen and B. Krostitz.
  Towards Solving Very Large Scale Train Timetabling Problems by Lagrangian Relaxation
  Proceedings of ATMOS 2008 - 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems, 2008.
• M. Armbruster, M. Fügenschuh, C. Helmberg, and A. Martin.
  A comparative Study of Linear and Semidefinite Branch-and-Cut Methods for Solving the Minimum Graph Bisection Problem
  Integer Programming and Combinatorial Optimization, Proceedings of the 13th International IPCO Conference, Bertinoro, Italy, May 2008, A. Lodi, A. Panconesi, G. Rinaldi (Eds.), Lecture Notes in Computer Science 5035, Springer 2008, pp. 112-124.
  Preprint
• M. Armbruster, M. Fügenschuh, C. Helmberg, and A. Martin.
  On the Graph Bisection Cut Polytope
  SIAM J. Discrete Math. (2008), Vol. 22, No. 3, pp. 1073-1098.
  (Preprint 2006-20, Technische Universität Chemnitz, Fakultät für Mathematik, November 2006.)
  
• F. Göring, C. Helmberg, and M. Wappler.
  Embedded in the Shadow of the Separator
  SIAM J. Optim. (2008), Vol. 19, No. 1, pp. 472-501.
  (Preprint 2005-12, Preprint 2005-12, Technische Universität Chemnitz, Fakultät für Mathematik, September 2005.)
  
• C. Helmberg and S. Röhl.
  A Case Study of Joint Online Truck Scheduling and Inventory Management for Multiple Warehouses
  Operations Research 55(4), 733-752, 2007.
  (Preprint 2005-3, Technische Universität Chemnitz, Fakultät für Mathematik, January 2005)
• C. Helmberg.
  A Cutting Plane Algorithm for Large Scale Semidefinite Relaxations
  in M. Grötschel (Ed.), Padberg Festschrift "The Sharpest Cut", MPS-SIAM 2004, pp. 233-256.
  abstract (http)

• C. Helmberg.
  Numerical Evaluation of SBmethod
  Mathematical Programming 95(2) (2003) pp. 381-406.
  Preprint

• C. Helmberg.
  Semidefinite Programming for Combinatorial Optimization
  Habilitationsschrift, TU Berlin, January 2000.
  ZIB-Report ZR-00-34, Konrad-Zuse-Zentrum Berlin, October 2000.
  abstract (http)

• C. Helmberg and K. C. Kiwiel.
  A Spectral Bundle Method with Bounds
  Mathematical Programming 93(2) (2002) pp. 173-194.
  Preprint

• C. Helmberg.
  Semidefinite programming
  European Journal of Operational Research (137)3 (2002) pp. 461-482.
  Preprint

• C. Helmberg and F. Oustry.
  Bundle methods to minimize the maximum eigenvalue function
  Handbook of Semidefinite Programming, H. Wolkowicz, R. Saigal and L. Vandenberghe (Eds.), Kluwer Academic Publishers 2000, pp. 307-337.

• C. Helmberg.
  The m-Cost ATSP
  Integer Programming and Combinatorial Optimization, Proceedings of the 7th International IPCO Conference, Graz, Austria, June 1999, G. Cornuéjols, R. E. Burkard, G. J. Woeginger (Eds.), Lecture Notes in Computer Science 1610, Springer 1999, pp.242-258.
  Preprint

• C. Helmberg, K. C. Kiwiel, and F. Rendl.
  Incorporating Inequality Constraints in the Spectral Bundle Method,
  Integer Programming and Combinatorial Optimization, Proceedings of the 6th International IPCO Conference, Houston, Texas, June 1998, R. E. Bixby, E. A. Boyd, R. Z. Rios-Mercado (Eds.), Lecture Notes in Computer Science 1412, Springer 1998, pp.423-435.
  Preprint

• C. Helmberg and F. Rendl.
  A Spectral Bundle Method for Semidefinite Programming,
  SIAM J. Opt. (2000) Vol. 10, No. 3, pp. 673-696.
  Preprint

• C. Helmberg.
  Fixing Variables in Semidefinite Relaxations,
  SIAM J. Matrix Anal. Appl. (2000) Vol. 21, No. 3, pp. 952-969.
  A preliminary version appeared in:
  Algorithms - Esa '97, Proceedings of the 5th Annual European Symposium, Graz, Austria, September 1997, R. Burkard, G. Woeginger (Eds.), Lecture Notes in Computer Science 1284, Springer 1997, pp. 259-270.
  Preprint

• C. Helmberg and R. Weismantel.
  Cutting Plane Algorithms for Semidefinite Relaxations,
  Fields Institute Communications, Volume 18, 1998, pp. 197-213.
  abstract (http)

• C. Helmberg, F. Rendl, and R. Weismantel.
  A Semidefinite Programming Approach to the Quadratic Knapsack Problem,
  J. of Combinatorial Optimization, Vol. 4, 2000, No. 2, pp. 197-215.
  Preprint; this is the full version of the next item below:

• C. Helmberg, F. Rendl, and R. Weismantel.
  Quadratic Knapsack Relaxations Using Cutting Planes and Semidefinite Programming,
  Integer Programming and Combinatorial Optimization, Proceedings of the 5th International IPCO Conference, Vancouver, June 1996, W. H. Cunningham, S. T. McCormick, and M. Queyranne (Eds.), Lecture Notes in Computer Science 1084, Springer 1996, pp.175-189.
  Preprint, see "A Semidefinite Programming Approach to the Quadratic Knapsack Problem" for the full version.

• C. Helmberg and F. Rendl.
  Solving Quadratic (0,1)-Problems by Semidefinite Programs and Cutting Planes,
  Mathematical Programming 82(1998) 291-315.
  Preprint

• C. Helmberg, S. Poljak, F. Rendl, and H. Wolkowicz.
  Combining Semidefinite and Polyhedral Relaxations for Integer Programs,
  Integer Programming and Combinatorial Optimization, Proceedings of the 4th International IPCO Conference, Denmark, May 1995, Egon Balas and Jens Clausen (Eds.), Lecture Notes in Computer Science 920, Springer 1995, pp.124-134.
  Preprint

• C. Helmberg.
  An Interior Point Method for Semidefinite Programming and Max-Cut Bounds,
  Ph.D.-thesis, Department of Mathematics, Graz University of Technology, Oct. 1994.

• C. Helmberg, F. Rendl, R.J. Vanderbei, and H. Wolkowicz.
  An Interior-Point Method for Semidefinite Programming,
  SIAM J. Optim., Vol. 6, No. 2, pp. 342-361, May 1996.
  Preprint

• C. Helmberg.
  Cutting Aluminium Coils with High Length Variabilities,
  Annals of Operations Research 57(1995)175-189.

• C. Helmberg, B. Mohar, S. Poljak, and F. Rendl.
  A Spectral Approach to Bandwidth and Separator Problems in Graphs,
  Linear and Multilinear Algebra, 1995, Vol. 39, pp. 73-90.
  Preprint

• D.W. Fellner and C. Helmberg.
  Best Approximate General Ellipses on Integer Grids,
  Comput. & Graphics, Vol. 18, No. 2, 1994, pp. 143-151.

• D.W. Fellner and C. Helmberg.
  Robust Rendering of General Ellipses and Elliptical Arcs,
  ACM Transactions on Graphics, Vol. 12, No. 3, July 1993, pp. 251-276.