Large-scale optimization problems appear naturally in many engineering fields such as machine learning, signal processing, image reconstruction, control, and bioinformatics. The research in this group is focused on efficient algorithms for solving such problems. The primary focus is on deterministic and stochastic operator splitting methods as they can scale to solve very large problems. We analyze convergence and performance of existing methods and use this insight to devise new algorithms with improved performance.
E. Ryu, A. Taylor, C. Bergeling, P. Giselsson, Operator Splitting Performance Estimation: Tight contraction factors and optimal parameter selection. Submitted.
M. Fält and P. Giselsson, Optimal Convergence Rates for Generalized Alternating Projections. In Proceedings of the 56th Conference on Decision and Control, Melbourne, Australia, Dec 2017.
P. Giselsson, Tight Global Linear Convergence Rate Bounds for Douglas-Rachford Splitting. Journal of Fixed-Point Theory and Applications, 2017. doi:10.1007/s11784-017-0417-1.
P. Giselsson and M. Fält, Envelope Functions: Unifications and Further Properties. Journal of Optimization Theory and Applications, 178(3):673 - 698, 2018.
P. Giselsson, and S. Boyd, Linear Convergence and Metric Selection in Douglas Rachford Splitting and ADMM. Transactions of Automatic Control. 62(2):532 - 544, February 2017.
P. Giselsson, M. Fält, and S. Boyd, Line Search for Averaged Operator Iteration. In Proceedings of the 55th Conference on Decision and Control, Las Vegas, USA, Dec 2016.
P. Giselsson, and S. Boyd, Metric Selection in Fast Dual Forward Backward Splitting. Automatica, 62:1-10, December 2015.