Bernd Kummer

from Wikipedia, the free encyclopedia

Bernd Kummer (* 1947 in Leipzig ) is a German mathematician and university professor .

Life

Studies and PhD

From 1965 to 1970 Kummer studied mathematics at the Humboldt University in Berlin . From 1970 to 1972 he completed a research course and then worked from 1972 to 1977 as a research assistant. In 1975 he received his doctorate as Dr. rer. nat. at the Humboldt University of Berlin with NN Worobjoff and Klaus Lommatzsch. His dissertation was on discrete positional games and a generalization of von Neumann-Morgenstern's concept of solutions for classic cooperative games .

Employment

Kummer completed his habilitation in 1977 with a thesis on global stability studies for parametric optimization tasks with František Nožička . From 1977 he was a lecturer and from 1993 professor at the Humboldt University, Faculty of Mathematics and Natural Sciences, optimization department .

Research stays

Research priorities

Kummer's main research areas are non-smooth analysis and optimization, stability and solution methods for optimization and game theory , fixed points of multivalued mappings .

From 2005 to 2009 he worked with Eberhard Bänsch, Carsten Carstensen, Dietmar Hömberg, Barbara Niethammer, Lutz Recke, Werner Römisch, Jürgen Sprekels on the project Analysis, Numerics and Optimization of Multi-Phase Problems . It was funded by the German Research Foundation and worked on jointly by the Humboldt University, the Weierstrass Institute for Applied Analysis and Stochastics (formerly the Academy of Sciences of the GDR ) and the Yachay Tech University, Ecuador .

Publications

As an author (selection)

  • Diethard Klatte , Bernd Kummer: Approximations and generalized Newton methods , 2018, Math. Program. 168 (1-2), pp. 673-716
  • Diethard Klatte, Bernd Kummer: On Calmness of the Argmin Mapping in Parametric Optimization Problems , 2015, J. Optimization Theory and Applications 165 (3), pp. 708-719
  • Bernd Bank, Jürgen Guddat , Diethard Klatte, Bernd Kummer, and Klaus Tammer: Non-Linear Parametric Optimization , Mathematical Textbooks and Monographs, Section II: Mathematical Monographs, Volume 58. Akademie-Verlag, Berlin, 1982. Also published by Birkhäuser, Basel-Boston, 1983. Birkhäuser, Softcover reprint of the original 1st ed. 1983, April 11, 2014, ISBN 3-0348-6330-6 , ISBN 978-3-0348-6330-8
  • Diethard Klatte, Bernd Kummer: Aubin property and uniqueness of solutions in cone constrained optimization , 2013, Math. Meth. Of OR 77 (3), pp. 291-304
  • Stephan Bütikofer, Diethard Klatte, Bernd Kummer: On second-order Taylor expansion of critical values , 2010, Cybernetika 46 (3), pp. 472–487
  • Diethard Klatte, Bernd Kummer: Optimization methods and stability of inclusions in Banach spaces , 2009, Math. Program. 117 (1-2), pp. 305-330
  • Bernd Kummer: Crash Course Optimization: Basic statements on necessary optimality conditions and stability , 2005, online
  • Christian Grossmann, Diethard Klatte, Bernd Kummer: Convergence of primal-dual solutions for the nonconvex log-barrier method without LICQ , 2004, Cybernetika 40 (5), pp. 571-584
  • Diethard Klatte, Bernd Kummer: Nonsmooth Equations in Optimization: Regularity, Calculus, Methods and Applications (Nonconvex Optimization and Its Applications Book 60) , Springer, May 31, 2002, ISBN 1-4020-0550-4 .
  • Diethard Klatte, Bernd Kummer: Strong stability in nonlinear programming revisited , 1999, J. Australian Mathem. Soc. Ser. B 40, pp. 336-352.
  • Bernd Kummer: Games on Graphs (International Series of Numerical Mathematics) (German Edition) , Birkhäuser, 1980, August 2, 2013, ISBN 3-0348-5482-X , ISBN 978-3-0348-5482-5
    • This book has been translated into Russian: Куммер Б. Игры на графах. (Games on graphs, 1979) [Djv- 1.4M] Перевод с немецкого С.Л. Печерского под редакцией Н.Н. Воробьева. Москва: Издательство "Мир". Редакция литературы по математическим наукам, 1982, online

As editor (selection)

  • Jürgen Guddat (Editor), Hubertus-Theophilus Jongen (Editor), Bernd Kummer (Editor): Parametric Optimization and Related Topics III (Approximation and Optimization) , Peter Lang GmbH, Internationaler Verlag der Wissenschaften, August 1, 1993, ISBN 978- 3-631-45799-3 .
  • Jürgen Guddat (editor), Hubertus-Theophilus Jongen (editor), Bernd Kummer (editor), František Nožička (editor): Parametric Optimization and Related Topics: v. 2 (Mathematical Research S.) , Wiley-VCH Verlag GmbH, March 25, 1991, ISBN 3-05-501290-9 .

Web links

Individual evidence

  1. ^ Parametric Optimization and Related Topics III at Peter Lang Verlagsgruppe. Retrieved July 26, 2019.
  2. ↑ a b c d e Prof. Dr. Bernd Kummer at HU Research Report 1997–1999. Retrieved July 26, 2019.
  3. ^ Bernd Kummer at Mathematics Genealogy Project. Retrieved July 27, 2019.
  4. ^ Bernd Kummer at Mathematics Genealogy Project. Retrieved July 27, 2019.
  5. ↑ Analysis, numerics and optimization of multi-phase problems at dfg.Retrieved on July 27, 2019.
personal data
SURNAME Grief, Bernd
BRIEF DESCRIPTION German mathematician and university professor
DATE OF BIRTH 1947
PLACE OF BIRTH Leipzig