Low-Rank Inducing Norms with Optimality Interpretations

Speaker: Christian Grussler
Affiliation: Lund University, Sweden

Abstract: 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. Today, one of the most widely used methods for solving these problems 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:

  1. Give a simple deterministic test if the solution to the convexified problem is a solution to a specific non-convex problem.
  2. Often finds solutions where the nuclear norm fails to give low-rank solutions.
  3. Allow us to analyze the convergence of non-convex proximal splitting algorithms with convex analysis tools.
  4. Provide a more efficient regularization than the traditional scalar multiplication of the nuclear norm.
  5. 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.

Biography:  Christian Grussler is a postdoc with the Department of Automatic Control at Lund University, Sweden. His current research interests include positive systems, model reduction, system identification and low-rank/sparse optimization. He received a Dipl.-Math. techn. degree (Industrial Mathematics) from TU Kaiserslautern, Germany and an M.Sc. degree (Engineering Mathematics) from Lund University in 2011. In 2017, he received a Ph.D. degree from Lund University.

For more information, contact Prof. Lieven Vandenberghe ()

Date(s) - Apr 27, 2017
11:00 am - 12:30 pm

E-IV Tesla Room #53-125
420 Westwood Plaza - 5th Flr., Los Angeles CA 90095