Research
I study the theoretical and computational foundations of optimization methods that remain useful when problems are nonsmooth, nonconvex, or distributionally uncertain.
When do first-order algorithms converge to meaningful solutions in genuinely nonsmooth games?
Stationarity, primal–dual balancing, and complexity guarantees for nonsmooth nonconvex–nonconcave problems.
How can robustness models remain both statistically meaningful and computationally tractable?
Optimization and statistical frameworks for reliable decisions under distribution shift and model uncertainty.
Which finite-dimensional algorithms preserve the geometry of optimization over probability measures?
Provable algorithms in Wasserstein geometry and computational methods for Gromov–Wasserstein problems.
How can optimization reveal and exploit structure in modern learning problems?
Optimization methods for graph learning, anomaly detection, experimental design, and structured data.