My research focuses on large-scale data analysis and optimization In particular, I design, analyze, and implement optimization algorithms for large-scale (data intensive) problems in statistics, machine learning, and computational science. My main mathematical tools draw upon: theoretical computer science, statistics, signal processing, matrix analysis, harmonic analysis, convex and nonconvex optimization, stochastic programming, and numerical linear algebra.
More broadly, I am usually interested in all things computational, where one can not only implement algorithms, but also prove some theorems!
Primary Projects and Research Areas
- Machine learning, data mining, computational statistics
- Inverse Problems in Signal Processing, Medical Imaging, Astronomy, Computer Vision
- Inexact Computation: Optimization under error and uncertainty
- Large-scale (continuous) optimization:
- Large-scale linear and quadratic programming
- Distributed and Parallel Nonlinear Optimization
- Large-scale nonsmooth convex and nonconvex optimization
- Search and retrieval in databases of structured objects (images, proteins, etc.)
- Matrix Analysis: matrix means, positive definite matrices, kernel function theory, etc.