Title: level set methods for convex optimization
Abstract: Convex optimization problems in a variety of applications have favorable objectives but complicating constraints, and first-order methods are not immediately applicable. We propose an approach that exchanges the roles of the objective and constraint functions, and instead approximately solves a sequence of parametric problems. We describe the theoretical and practical properties of this approach for a broad range of problems, including low-rank semidefinite optimization problems.
Joint work with A. Aravkin, J. Burke, D. Drusvyatskiy, S. Roy.
Bio: Michael P. Friedlander is a 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, 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.