Proximal Algorithms and Their Applications
Dr.Minh N. Dao (CARMA, University of Newcastle)
Dr. Minh N. Dao received the Ph.D. degree in applied mathematics from the University of Toulouse, France in 2014. He was a Lecturer at Hanoi National University of Education, Vietnam from 2004 to 2010, a Lecturer and Research Assistant at National Institute of Applied Sciences (INSA) in Toulouse, France from 2013 to 2014, and a Postdoctoral Fellow at The University of British Columbia, Canada from 2014 to 2016.
He is currently a Research Associate in the Priority Research Centre for Computer-Assisted Research Mathematics and its Applications (CARMA) at The University of Newcastle, Australia. His research interests include nonlinear optimization, nonsmooth analysis, iterative methods, monotone operator theory, control theory, and operations research. In 2017, he received the Annual Best Paper Award from the Journal of Global Optimization.
Proximal algorithms are iterative optimization algorithms that split complex problems into a series of simpler subproblems. They rely on evaluating proximity operators -- a natural extension of the notion of projection operators. Due to their simplicity and flexibility, these algorithms have been applied to a wide range of feasibility and optimization problems arising in signal and image processing, operations research, data science, and machine learning. In this talk, we report our recent progress in understanding the behavior of proximal algorithms including projection algorithms, the proximal point algorithm, forward--backward splitting, and Douglas--Rachford splitting. In particular, we provide new results on the rate of convergence in the possibly nonconvex setting.
Analysis of proximal algorithms for feasibility and optimization problems: Part I
Analysis of proximal algorithms for feasibility and optimization problems: Part II
Analysis of proximal algorithms for feasibility and optimization problems: Part III