University of Birmingham > Talks@bham > Optimisation and Numerical Analysis Seminars > A quotient geometry on the manifold of fixed-rank positive-semidefinite matrices

A quotient geometry on the manifold of fixed-rank positive-semidefinite matrices

Add to your list(s) Download to your calendar using vCal

  • UserEstelle Massart (NPL-postdoc, University of Oxford)
  • ClockWednesday 11 March 2020, 12:00-13:00
  • HousePhysics West 103.

If you have a question about this talk, please contact Sergey Sergeev.

Riemannian optimization aims to design optimization algorithms for constrained problems, where the constraints enforce the variables to belong to a Riemannian manifold. Classical examples of Riemannian manifolds include, e.g., the set of orthogonal matrices, the set of subspaces of a given dimension (called the Grassman manifold), and the set of fixed-rank matrices.

After a quick introduction to Riemannian optimization, and more specifically Riemannian gradient descent (RGD), we will present the tools needed to run RGD on the manifold of fixed-rank positive-semidefinite matrices, seen as a quotient of the set of full-rank rectangular matrices by the orthogonal group. We will also present recent results about related geometrical tools on that manifold. This manifold is particularly relevant when dealing with low-rank approximations of large positive-(semi)definite matrices.

This talk is part of the Optimisation and Numerical Analysis Seminars series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

Talks@bham, University of Birmingham. Contact Us | Help and Documentation | Privacy and Publicity.
talks@bham is based on talks.cam from the University of Cambridge.