Information Geometry and its Applications III

Abstract Atsumi Ohara

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Atsumi Ohara  (Osaka University, Japan)
Friday, August 06, 2010, room Hörsaal 1
Computation, complexity and curvature in information geometry

Euler-Schouten embedding curvature (the second fundamental form) plays an important role in not only geometry itself but also computational mathematics or scientific computing.

A well-known example would be a relation with performance of estimators in statistical inference, which was elucidated by the Amari's seminal work.

In this talk, we show that iteration-complexity of an interior-point algorithm for conic linear programming problems (e.g., linear or semidefinite programming and so on) is characterized by dual embedding curvature of a feasible region, or specifically, what is called a central trajectory.

In an extreme case where the curvature vanishes, we can construct a formula for an optimal solution, and hence, need no iterations to solve it.

The related topics will also be presented.

The talk is partly based on a joint work with Takashi Tsuchiya at ISM Japan.

 

Date and Location

August 02 - 06, 2010
University of Leipzig
Augustusplatz
04103 Leipzig
Germany

Scientific Organizers

Nihat Ay
Max Planck Institute for Mathematics in the Sciences
Information Theory of Cognitive Systems Group
Germany
Contact by Email

Paolo Gibilisco
Università degli Studi di Roma "Tor Vergata"
Facoltà di Economia
Italy
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František Matúš
Academy of Sciences of the Czech Republic
Institute of Information Theory and Automation
Czech Republic
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Scientific Committee

Shun-ichi Amari
RIKEN
Brain Science Institute, Mathematical Neuroscience Laboratory
Japan
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Imre Csiszár
Hungarian Academy of Sciences
Alfréd Rényi Institute of Mathematics
Hungary
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Dénes Petz
Budapest University of Technology and Economics
Department for Mathematical Analysis
Hungary
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Giovanni Pistone
Collegio Carlo Alberto, Moncalieri
Italy
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Administrative Contact

Antje Vandenberg
Max Planck Institute for Mathematics in the Sciences
Contact by Email
Phone: (++49)-(0)341-9959-552
Fax: (++49)-(0)341-9959-555

05.04.2017, 12:42