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Intensive Course Set-Valued Numerical Analysis and Optimal Control


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-Project "Center of Excellence for Applications of Mathematics")


Handout (last update: 29 Sep, 2005) PDF File


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:

 

Robert J. Aumann: Integrals of Set-Valued Functions.
Journal of Mathematical Analysis and Applications 12, no. 1, pp. 1-12 (1965).
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)
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)
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

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


Links to Books on Numerical Analysis and ODEs

Numerical Recipes (information on books and software)
Numerical Recipes in C++ (W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery)
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

Matlab and Simulink
Scilab
Octave


Links to Programming Tools

GNU Compiler Collection (GCC)
MinGW (GCC port for Windows)
Bloodshed (IDE for Windows, includes GCC-port)
Data Display Debugger (Debugger for Unix)


LaTeX-Package for Presentations

(used for the intensive course)

Beamer


Computational Geometry

Books (incl. Software)

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


Software and Archives for Computational Geometry

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