|Speaker: Dr. Patrick Johnstone, MSIS Department of the Rutgers Business School.
Title: Projective Splitting: A New Breed of First-Order Proximal Algorithms
Date and Time: Friday, February 28th, 3.30pm – 4.30pm, 2020 (Talk & Q/A)
Location: AGR Building 15, level 3, room 10 (Request for remote connect email@example.com)
|Abstract: Projective splitting is a proximal operator splitting framework for solving convex optimization problems and monotone inclusions. Unlike many operator splitting methods, projective splitting is not based on a fixed-point iteration. Instead, at each iteration a separating hyperplane is constructed between the current point and the primal-dual solution set. This gives more freedom in terms of stepsize selection, incremental updates, and asynchronous parallel computation. Despite these advantages, projective splitting had two important drawbacks which we have rectified in this work. First, the method uses calculations entirely based on the proximal operator of the functions in the objective. However, for many functions this is intractable. We develop new calculations based on forward steps – explicit evaluations of the gradient – whenever the gradient is Lipschitz continuous. This extends the scope of the method to a much wider class of problems. Second, no convergence rates were previously known for the method. We derive an O(1/k) rate for convex optimization problems, which is unimprovable for this algorithm and problem class. Furthermore, we derive a linear convergence rate under certain strong convexity and smoothness conditions.
Bio: Patrick R. Johnstone is a postdoctoral associate in the MSIS Department of the Rutgers Business School where he is advised by Prof. Jonathan Eckstein. In May 2017 he received his PhD in Electrical and Computer Engineering from the University of Illinois at Urbana-Champaign (advised by Prof. Pierre Moulin). He also received the MSc degree in ECE from UIUC. He received the BSc degree in Electrical Engineering from the University of New South Wales (UNSW) in Sydney, Australia. At UNSW he received the university medal, given to the top student in electrical engineering. He has worked as a research intern at Qualcomm Research, Rambus Labs, and CSIRO. For his work at Qualcomm, he received the Roberto Padovani award for outstanding interns. His research interests are in continuous optimization, first-order proximal splitting methods, parallel and distributed algorithms, machine learning, and signal processing.