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
04103 Leipzig

Scientific Organizers

Nihat Ay
Max Planck Institute for Mathematics in the Sciences
Information Theory of Cognitive Systems Group
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Paolo Gibilisco
Università degli Studi di Roma "Tor Vergata"
Facoltà di Economia
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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
Brain Science Institute, Mathematical Neuroscience Laboratory
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Imre Csiszár
Hungarian Academy of Sciences
Alfréd Rényi Institute of Mathematics
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Dénes Petz
Budapest University of Technology and Economics
Department for Mathematical Analysis
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Giovanni Pistone
Collegio Carlo Alberto, Moncalieri
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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