
CommNetS seminar
Tue, Apr 25, 2017 @ 02:00 PM  03:00 PM
Ming Hsieh Department of Electrical and Computer Engineering
Conferences, Lectures, & Seminars
Speaker: Dr. Christian Grussler, Lund University
Talk Title: LowRank Inducing Norms with Optimality Interpretations
Series: CommNetS
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, lowrank approximation and many more. Today, one of the most widely used methods for solving these problems is socalled 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 socalled lowrank 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 nonconvex problem.
ii) Often finds solutions where the nuclear norm fails to give lowrank solutions.
iii) Allow us to analyze the convergence of nonconvex 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.
vi) In particular, all the results can be generalized to socalled atomic norms.
Biography: Christian Grussler is a postdoc at the Department of Automatic Control at Lund University, Sweden. His current research interests include positive systems, model reduction, system identification and lowrank/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 under the guidance of Anders Rantzer and Pontus Giselsson.
Host: Prof. Mihailo Jovanovic
Location: Hughes Aircraft Electrical Engineering Center (EEB)  132
Audiences: Everyone Is Invited
Contact: Annie Yu