The Department of Mathematical Sciences is pleased to announce that Yangyang Xu, assistant professor of mathematical sciences, has received a new grant from the National Science Foundation (NSF) in the area of Computational and Data-Enabled Science and Engineering in Mathematical and Statistical Sciences (CDS&E-MSS). He will use the three-year, $250,000 award to study "Information-Based Complexity Analysis and Optimal Methods for Saddle-Point Structured Optimization."

The central focus of Professor Xu's project involves designing provably-efficient algorithms for solving saddle-point structured optimization problems. These problems arise from many applications, such as mechanical design that involves hard physical constraints, statistical learning that involves fairness constraints, and robust machine learning. The constraints and robustness are important in the applications. Without robustness consideration, a well-trained deep learning model is prone to adversarial attack. For example, a model that yields almost perfect prediction accuracy can recognize a slightly-contaminated STOP sign as a speed-limit sign. Different from standard minimization problems with a smooth objective, saddle-point structured problems are generally non-smooth and thus more challenging. Nevertheless, because of the saddle-point structure, they are often easier to solve than general non-smooth minimization problems. Therefore, it is very important to exploit the saddle-point structure in designing efficient algorithms. Professor Xu and his students aim to design optimal first-order (or gradient-type) methods for these structured problems, through establishing lower complexity bounds of first-order methods and exploring various acceleration techniques in the algorithm design in order to achieve the fastest convergence.

Professor Xu received his Ph.D. in mathematics at Rice University. He held postdoctoral appointments at the University of Minnesota and the University of Waterloo, before joining the Department of Mathematical Sciences at Rensselaer in August, 2017. This NSF award will provide strong external support for Professor Xu's already active research program.