Research Summary
Optimization plays an important role in engineering, science, and health care.
My research focuses on the design and analysis of (stochastic) first-order methods for nonlinear optimization. I aim to develop algorithms that are both simple and efficient. A central idea is to make difficult problems more tractable through exact penalization, smoothing, and convexification.
These transformations allow us to use well-established algorithmic frameworks, with strong theoretical guarantees and practical performance. My interests include:
- First-order methods for large-scale nonconvex, nonsmooth constrained optimization.
- Stochastic (sub)gradient methods for statistics and machine learning.
- Iteration, oracle, and computational complexity.
- Applications in AI and machine learning, including fairness, deep neural networks, distributed robust optimization, decentralized distributed learning, semi-supervised learning, bilevel optimization, minimax problems, and large language models.
Current interests
In order of current priority:
- Computing directional stationary points of nonconvex nonconcave minimax problems.
- Stochastic first-order methods for min-sum-max problems: iteration complexity and convergence.
- Decentralized optimization.
- Lower bounds for functionally constrained problems.
- Applications to Wasserstein distributionally robust optimization, fairness-constrained problems, and large language models.
Large language models
I have regularly followed research on large language models since August 2022. I interact with them almost every day and use them to support writing, mathematical reasoning, and example construction.
My current impression is that GPT 6 is not excellent at writing.