Research Summary

Optimization plays a significant role in many areas such as engineering, science and health care. My research focuses on the design and analysis of (stochastic) first‑order methods for nonlinear optimization problems. I strive to develop algorithms that are simple yet efficient. The core idea is to simplify a complex problem by transforming it into a simpler one, thereby making the overall algorithm more tractable. Representative examples of such transformations include exact penalization, smoothing and convexification. These techniques allow us to apply well‑established algorithmic frameworks and yield both strong theoretical guarantees and compelling practical performance.

I am particularly interested in the following topics:

• First‑order methods for large‑scale nonconvex (nonsmooth) constrained optimization;
• Stochastic (sub)gradient methods for statistical and machine learning;
• Complexity analysis (iteration, oracle and computational);
• Applications such as fairness in AI, deep neural networks, distributed robust optimization, decentralized distributed learning, semi‑supervised learning, bilevel optimization, minimax problems and large language models.

I’ve regularly read research on large language models since August 2022. I speak to them almost every day. I use LLMs to support my work in writing, mathematical reasoning and example construction. GPT 4.5 is excellent in writing.