Publications (Prof. Dür)

Preprints

Mathematical papers in international journals

  1. Naomi Shaked-Monderer, Mirjam Dür, and Abraham Berman:
    Complete positivity over the rationals.
    Pure and Applied Functional Analysis 3 (2018), 681-691.
  2. Mirjam Dür, Bolor Jargalsaikhan, and Georg Still:
    Genericity results in linear conic programming - a tour d'horizon.
    Mathematics of Operations Research 44 (2017), 77-94.
  3. Cristian Dobre, Mirjam Dür, Leonhard Frerick, and Frank Vallentin:
    A copositive formulation for the stability number of infinite graphs.
    Mathematical Programming 160 (2016), 65-83. (arXiv preprint).
  4. Naomi Shaked-Monderer, Abraham Berman, Mirjam Dür, and Rajesh Kannan:
    SPN completable graphs.
    Linear Algebra and its Applications 498 (2016), 58-73.
  5. Abraham Berman, Mirjam Dür, Naomi Shaked-Monderer, and Julia Witzel:
    Cutting planes for semidefinite relaxations based on triangle-free subgraphs.
    Optimization Letters 10 (2016), 433-446.  
  6. Mirjam Dür, Bolor Jargalsaikhan, and Georg Still:
    First order solutions in conic programming.
    Mathematical Methods of Operations Research 82 (2015), 123-142.
  7. Abraham Berman, Mirjam Dür, and Naomi Shaked-Monderer:
    Open problems in the theory of completely positive and copositive matrices.
    Electronic Journal of Linear Algebra 29 (2015), 46-58.
  8. Julia Sponsel and Mirjam Dür:
    Factorization and Cutting Planes for Completely Positive Matrices by Copositive Projection.
    Mathematical Programming 143 (2014), 211-229.
  9. Mirjam Dür and Jean-Baptiste Hiriart-Urruty:
    Testing copositivity with the help of difference-of-convex optimization.
    Mathematical Programming 140 (2013), 31-43.
  10. Peter J.C. Dickinson, Mirjam Dür, Luuk Gijben, and Roland Hildebrand:
    Scaling relationship between the copositive cone and Parrilo's first level approximation.
    Optimization Letters 7 (2013), 1669-1679. Received 2013 OPTL Best Paper Award.
  11. Peter J.C. Dickinson, Mirjam Dür, Luuk Gijben, and Roland Hildebrand:
    Irreducible elements of the copositive cone.
    Linear Algebra and its Applications, 439 (2013), 1605-1626.
  12. Faizan Ahmed, Mirjam Dür, and Georg Still:
    Copositive Programming via Semi-Infinite Optimization.
    Journal of Optimization Theory and Applications, 159 (2013), 322-340.
  13. Peter J.C. Dickinson and Mirjam Dür:
    Linear-time complete positivity detection and decomposition of sparse matrices.
    SIAM Journal on Matrix Analysis and Applications 33 (2012), 701-720.
  14. Julia Sponsel, Stefan Bundfuss, and Mirjam Dür:
    An improved algorithm to test copositivity.
    Journal of Global Optimization 52 (2012), 537-551.
  15. Julius Zilinskas and Mirjam Dür:
    Depth-first Simplicial Partition for Copositivity Detection, with an Application to MaxClique.
    Optimization Methods and Software 26 (2011), 499-510.
  16. Mirjam Dür:
    Copositive Programming - a Survey.
    In: M. Diehl, F. Glineur, E. Jarlebring, W. Michiels (Eds.), Recent Advances in Optimization and its Applications in Engineering, Springer 2010, pp. 3-20.
    This paper is available as sample pages from the book.
  17. Samuel Burer, Kurt M. Anstreicher, and Mirjam Dür:
    The Difference Between 5 x 5 Doubly Nonnegative and Completely Positive Matrices.
    Linear Algebra and its Applications 431 (2009), 1539-1552.
  18. Stefan Bundfuss and Mirjam Dür:
    An Adaptive Linear Approximation Algorithm for Copositive Programs.
    SIAM Journal on Optimization 20 (2009), 30-53.
  19. Stefan Bundfuss and Mirjam Dür:
    Copositive Lyapunov Functions for Switched Systems over Cones.
    Systems and Control Letters 58 (2009), 342-345.
  20. Mirjam Dür and Georg Still:
    Interior Points of the Completely Positive Cone.
    Electronic Journal of Linear Algebra 17 (2008), 48-53.
  21. Stefan Bundfuss and Mirjam Dür:
    Algorithmic Copositivity Detection by Simplicial Partition.
    Linear Algebra and its Applications 428 (2008), 1511-1523.
  22. Mirjam Dür, Charoenchai Khompatraporn, and Zelda B. Zabinsky:
    Solving Fractional Problems with Dynamic Multistart Improving Hit-and-Run.
    Annals of Operations Research 156 (2007), 25-44.
  23. Mirjam Dür and Volker Stix:
    Probabilistic Subproblem Selection in Branch-and-Bound Algorithms.
    Journal of Computational and Applied Mathematics 182 (2005), 67-80.
  24. William P. Baritompa, Mirjam Dür, Eligius M.T. Hendrix, Lyle Noakes, Wayne J. Pullan, and Graham R. Wood:
    Matching Stochastic Algorithms to Objective Function Landscapes.
    Journal of Global Optimization 31 (2005), 579 - 598.
  25. Mirjam Dür:
    A Parametric Characterization of Local Optimality.
    Mathematical Methods of Operations Research 57 (2003), 101-109.
  26. Mirjam Dür:
    A Class of Problems where Dual Bounds Beat Underestimation Bounds.
    Journal of Global Optimization 22 (2002), 49-57.
  27. Mirjam Dür:
    Conditions Characterizing Minima of the Difference of Functions.
    Monatshefte für Mathematik 134 (2002), 295-303.
  28. Mirjam Dür:
    Dual Bounding Procedures Lead to Convergent Branch-and-Bound Algorithms.
    Mathematical Programming 91 (2001), 117-125.
  29. Mirjam Dür, Reiner Horst and Nguyen Van Thoai:
    Solving Sum-of-Ratios Fractional Programs.
    Optimization 49 (2001), 447-466.
  30. Immanuel M. Bomze, Mirjam Dür, Etienne De Klerk, Cornelis Roos, Arie Quist, and Tamas Terlaky:
    On Copositive Programming and Standard Quadratic Optimization Problems.
    Journal of Global Optimization 18 (2000), 301-320.
  31. Mirjam Dür, Reiner Horst and Marco Locatelli:
    Necessary and Sufficient Global Optimality Conditions for Convex Maximization Revisited.
    Journal of Mathematical Analysis and Applications 217 (1998), 637-649.
  32. Mirjam Dür and Reiner Horst:
    Lagrange-Duality and Partitioning Techniques in Nonconvex Global Optimization.
    Journal of Optimization Theory and Applications 95 (1997), 347-369.

Applied papers

  1. Susanne Pape, Franziska Hoffgaard, Mirjam Dür and Kay Hamacher:
    Distance Dependency And Minimum Amino Acid Alphabets for Decoy Scoring Potentials.
    Journal of Computational Chemistry, 34 (2013), 10-20.
  2. Mirjam Dür and Nicole Nowak:
    Packing Solar Cells on a Roof.
    Optimization and Engineering 10 (2009), 397-408.

Patent

  1. Alexander Martin, Armin Fügenschuh, Mirjam Dür, Christine Schönberger, Samuel Schabel, Klaus Villforth:  Verfahren zum Einstellen und/oder Optimieren einer einen Gutstoff von einem Schlechtstoff trennenden Sortieranlage und Sortieranlage.
    Deutsches Patent Nr. 10 2008 013 034, erteilt am 17. 9. 2009.

Miscellaneous publicatons

  • Mirjam Dür (Reporter): Oberwolfach Report 52/2017.
  • Patrick Groetzner and Mirjam Dür
    Factorization for completely positive matrices based on projection approaches.
    Oberwolfach Report No. 52/2017, pp. 19-21.
  • Mirjam Dür and Patrick Groetzner:
    A factorization heuristic for completely positive matrices.
    Oberwolfach Report No. 46/2015, pp. 2721-2723.
  • Immanuel M. Bomze, Mirjam Dür and Chung-Piaw Teo: Copositive Optimization.
    OPTIMA 89, Newsletter of the Mathematical Optimization Society, August 2012, pp. 2-8.
  • Mirjam Dür and Chris Tofallis: Neutral Data Fitting from an Optimisation Viewpoint.
    Proceedings of the International Workshop on Global Optimization 2005 in Almeria, Spain, pp. 91-96.
  • Mirjam Dür: Review of the book Convex Optimization by Stephen Boyd and Lieven Vandenberghe.
    Mathematical Methods of Operations Research 61 (2005), 521-522.
  • Mirjam Dür: Review of the book Mathematics of Optimization: Smooth and Nonsmooth Case by G. Giorgi, A. Guerraggio, and J. Thierfelder.
    Mathematical Methods of Operations Research 61 (2005), 171-172.

PhD thesis

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