COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > CUED Control Group Seminars > Low-Rank Inducing Norms with Optimality Interpretations

## Low-Rank Inducing Norms with Optimality InterpretationsAdd to your list(s) Download to your calendar using vCal - Christian Grussler, University of Lund
- Thursday 01 June 2017, 14:00-15:00
- Cambridge University Engineering Department, LR12.
If you have a question about this talk, please contact Tim Hughes. This talk is on optimization problems which are convex apart from a sparsity/rank constraint. These problems are often found in the context of compressed sensing, linear regression, matrix completion, low-rank approximation and many more. Since these problems are generally NP-hard, today, one of the most widely used methods for solving them is so-called nuclear norm regularization. Despite the nice probabilistic guarantees of this method, this approach often fails for problems with structural constraints. In this talk, we will present an alternative by introducing the family of so-called low-rank inducing norms as convexifiers. Each norm is the convex envelope of a unitarily invariant norm plus a rank constraint. Therefore, they have several interesting properties, which will be discussed throughout the talk. They: i. Give a simple deterministic test if the solution to the convexified problem is a solution to a specific non-convex problem. ii. Often finds solutions where the nuclear norm fails to give low-rank solutions. iii. Allow us to analyze the convergence of non-convex proximal splitting algorithms with convex analysis tools. iv. Provide a more efficient regularization than the traditional scalar multiplication of the nuclear norm. v. Leads to a different interpretation of the nuclear norm than the one that is traditionally presented. In particular, all the results can be generalized to so-called atomic norms. 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, LR12
- Cambridge talks
- Centre for Smart Infrastructure & Construction
- Chris Davis' list
- 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
- rp587
Note that ex-directory lists are not shown. |
## Other listsCambridge Lovelace Hackathons NanoScience Seminar Biodiversity and genomics## Other talksThe role of Birkeland currents in the Dungey cycle Modeling and understanding of Quaternary climate cycles Hide and seek: medieval creatures on the manuscript page Dispersion for the wave and the Schrodinger equations outside strictly convex obstacles |