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Workshop

Computation, complexity and curvature in information geometry

  • Atsumi Ohara (Osaka University, Japan)
Raum n.n. Universität Leipzig (Leipzig)

Abstract

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.

conference
8/2/10 8/6/10

Information Geometry and its Applications III

Universität Leipzig Raum n.n.

Antje Vandenberg

Max-Planck-Institut für Mathematik in den Naturwissenschaften Contact via Mail

Nihat Ay

Max Planck Institute for Mathematics in the Sciences, Germany

Paolo Gibilisco

Università degli Studi di Roma "Tor Vergata", Italy

František Matúš

Academy of Sciences of the Czech Republic, Czech Republic