Intensive Course

"Set-Valued Numerical Analysis and Optimal Control"

Borovets and Sofia, Bulgaria, 4-15 Sep, 2005

Organizer: Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences in Sofia

(funded by DAAD-Programme "Center of Excellence for Applications of Mathematics" within the Stability Pact for South Eastern Europe, Academic Reconstruction [PDF])

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Handout (last update: 29 Sep, 2005)

one page per sheet
two pages per sheet
changes to previous version

Nobelprize for Economics 2005 for R. J. Aumann

Robert J. Aumann has won the Nobelprize for Economics 2005 together with Thomas C. Schelling. Main justifications are his contributions to game theory and to the study of competetive equilibria. He also studied 1965 the Aumann's integral which was studied in the intensive course. His primary motivation for this research on the integral was game theory in economics, cf. the following articles:

bullet Robert J. Aumann: Integrals of Set-Valued Functions.  Journal of Mathematical Analysis and Applications 12, no. 1, pp. 1-12 (1965).
bullet Robert J. Aumann: Existence of Competitive Equilibria in Markets with a Continuum of Traders.  Econometrica 34, no. 1, pp. 1-17 (1966).  (main reason for the study of Aumann's integral)
bullet Robert J. Aumann, M. Perles: A Variational Problem Arising in Economics.  Journal of Mathematical Analysis and Applications 11, pp. 488-503 (1965).  (cites the work of Aumann's integral)
bullet Robert J. Aumann: Markets with a Continuum of Traders.  Econometrica 32, no. 1-2, pp. 39-50 (1964).  (previous work before Econometrica 34 which motivates the publication on the competitive equilibria)

Links to Software

Links to Archives for Mathematical Software

bullet Guide to Available Mathematical Software (GAMS)
bullet Netlib
bullet Decision Tree for Optimization Software
bullet NEOS Guide
bullet ZIB Software (ZIB = Konrad-Zuse-Center for Computer Science in Berlin)

Links to Books on Numerical Analysis and ODEs

bullet Numerical Recipes (information on books and software)  Numerical Recipes in C++ (W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery)
bullet ODE Software (information on books and software)  Solving Ordinary Differential Equations I & II et al. (E. Hairer, G. Wanner, C. Lubich, S. P. Norsett)

Links to Matlab and Clones

bullet Matlab and Simulink
bullet Scilab
bullet Octave

Links to Programming Tools

bullet GNU Compiler Collection (GCC)
bullet MinGW (GCC port for Windows)
bullet Code::Blocks (IDE for Windows, Mac and Linux, includes GCC-port)
bullet Bloodshed (older IDE for Windows, includes GCC-port)
bullet Data Display Debugger (Debugger for Unix)

LaTeX-Package for Presentations

(used for the intensive course)
bullet Beamer

Computational Geometry

Books (incl. Software)

bullet Computational Geometry: Algorithms and Applications (M. de Berg, O. Schwarzkopf, M. van Kreveld, M. Overmars)
bullet Computational Geometry in C (J. O'Rourke)

Software and Archives for Computational Geometry

bullet Directory of Computational Geometry
bullet Computational Geometry Algorithms Library (CGAL, huge C++ library)
bullet Porta (software around polyhedrons)
bullet qhull (software for convex hull algorithms, triangulations, Voronoi diagrams, ...)

Matthias Gerdts and Robert Baier

See also our original webpage of Matthias Gerdts.

Last modified: Mar 24, 2011, original version: Wed Oct 21 18:40:00 MET 2005

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