Dr. Lan’s research interests lie in theory, algorithms and applications of stochastic optimization and nonlinear programming. Most of his current research concerns the design of efficient algorithms with strong theoretical performance guarantees and superior practical performance for solving challenging optimization problems. He is actively pursuing the application of stochastic and nonlinear optimization in large-scale data analysis, including machine learning, image processing and simulation input/output analysis.
- National Science Foundation (CMMI-1000347), “Theory and Applications of Stochastic First-order Methods for Large-Scale Stochastic Convex Optimization”, May 2010 – April 2014.
- Office of Naval Research (ONR N00014-13-1-0036), “Dynamic and Adaptive Sensor Operations Under Uncertainty”, Jan. 2013 – Dec. 2015. (with Cole Smith).
- National Science Foundation (CMMI-1254446), “CAREER: Reduced-order Methods for Big-Data Challenges in Nonlinear and Stochastic Optimization”, Jan 2013 – Dec. 2017.
- National Science Foundation (DMS-1319050), “Accelerated Algorithms for a Class of Saddle Point problems and Variational Inequalities”, Sep. 2013 – Aug. 2016. (with Yunmei Chen).
- National Science Foundation (CMMI-1537414), “Gradient Sliding Schemes for Large-scale Optimization and Data Analysis”, Oct. 2015 – Sep. 2018.