Rank-preserving optimization on the cone of positive semidefinite matrices: a geometric approach

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• Rodolphe Sepulchre, University of Liege, Belgium
• Wednesday 19 May 2010, 14:30-15:30
• CAP Seminar Room .

If you have a question about this talk, please contact Alessandro Astolfi.

The talk is an introduction to a recent computational framework for optimization over the set of fixed rank positive semidefinite matrices. The foundation is geometric and the motivation is algorithmic, with a bias towards low-rank computations in large-scale problems. We will describe two quotient riemannian geometries that are rooted in classical matrix factorizations and that lead to rank-preserving efficient computations in the cone of symmetric positive definite matrices. The field of applications is vast, and the talk will survey recent developments that illustrate the potential of the approach in large-scale computational problems encountered in control, optimization, and machine learning. The talk is introductory and requires no particular background in Riemannian geometry.

This talk is part of the Control and Power Seminars series.

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