Gauges, Sparsity, and Spectral Optimization

Tuesday, October 27, 2015 - 1:25pm - 2:25pm
Lind 305
Michael Friedlander (University of California)
Gauge optimization is the class of problems for finding the element of a convex set that is minimal with respect to a gauge (e.g., the least-norm solution of a linear system). These conceptually simple problems appear in a remarkable array of applications of sparse optimization. Their structure allows for a special kind of duality framework that can lead to new algorithmic approaches to challenging problems. Low-rank spectral optimization problems that arise in two signal-recovery application, phase retrieval and blind deconvolution, illustrate the benefits of the approach.

Michael Friedlander is Professor of Mathematics at the University of California, Davis. He received his PhD in Operations Research from Stanford University in 2002, and his BA in Physics from Cornell University in 1993. From 2002 to 2004 he was the Wilkinson Fellow in Scientific Computing at Argonne National Laboratory. He has held visiting positions at UCLA's Institute for Pure and Applied Mathematics (2010), and at Berkeley's Simons Institute for the Theory of Computing (2013). He serves on the editorial boards of SIAM J. on Optimization, SIAM J. on Matrix Analysis and Applications, SIAM J. on Scientific Computing, Mathematical Programming, and Mathematical Programming Computation. His research is primarily in developing numerical methods for large-scale optimization, their software
implementation, and applying these to problems in signal processing and machine learning.