A Riemannian approach to large scale constrained least squares with symmetries

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

• Bamdev Mishra, University of Liege/ University of Cambridge
• Thursday 08 May 2014, 14:00-15:00
• Cambridge University Engineering Department, LR6.

If you have a question about this talk, please contact Tim Hughes.

Least squares optimization on a manifold of equivalence relations, i.e., in the presence of symmetries, appears  in many fields. Two fundamental examples are the generalized eigenvalue problem, a least-square problem with orthogonality constraints, and the matrix completion problem, a least-square problem with rank constraints. The large scale nature of these problems requires us to exploit the problem structure as much as possible. The presentation deals with these structures.

Riemannian optimization has gained much popularity in the recent years because of the particular nature of the orthogonality and rank constraints. Previous work on Riemannian optimization has mostly focused on the search space, exploiting the differential geometry of the constraint but disregarding the role of the cost function.

We show a basic connection between sequential quadratic programming and Riemannian gradient optimization and address the general question of selecting a metric in Riemannian optimization in a way that not only exploits the constraints but also the cost function, that is, exploits the least squares problem structure. 

The proposed method of selecting a Riemannian metric is shown to be particularly insightful and efficient in quadratic optimization with orthogonality and rank constraints, which covers most current applications of Riemannian optimization in matrix manifolds. 

Keywords: Riemannian optimization Sequential quadratic programming, Metric, Preconditioning, Orthogonality, Low-rank

This talk is part of the CUED Control Group Seminars series.

This talk is included in these lists:

• All Talks (aka the CURE list)
• CUED Control Group Seminars
• Cambridge Centre for Data-Driven Discovery (C2D3)
• Cambridge University Engineering Department Talks
• Cambridge University Engineering Department, LR6
• Cambridge talks
• Centre for Smart Infrastructure & Construction
• Chris Davis' list
• Computational Continuum Mechanics Group Seminars
• Featured lists
• Information Engineering Division seminar list
• Interested Talks
• School of Technology
• Signal Processing and Communications Lab Seminars
• Trust & Technology Initiative - interesting events
• bld31
• ndk22's list
• ob366-ai4er
• rp587

Note that ex-directory lists are not shown.