The interest in large-scale optimization methods has recently grown remarkably due to
their application in diverse practical problems including machine learning, statistics and
data science. Recent works have shown that the introduction of randomization techniques
such as random shuffling in optimization algorithms would result in more efficient and
accurate results. Yet, the mathematical justification of this is still lacking which servers as
an obstruction on understanding the randomization techniques and developing new and
efficient numerical methods.
This project aims to introduce randomization techniques into the operator splitting
algorithms for the more general nonconvex problems (such as the proximal gradient
methods and the Douglas-Rachford algorithm). In particular, it will focus on how to use
randomization techniques to improve current splitting algorithms for nonconvex
The University of New South Wales
Xiaoyu Li is a fourth-year undergraduate student at the University of New South Wales majoring in mathematics and computer science. His research focus lies between applied mathematics and computer science, with interests in mathematical optimization and theoretical machine learning. He is working towards attaining a doctorate in mathematics and hopes to be qualified enough to become a mathematician someday, which would be a great honor.