About me

I am Lexiao Lai 赖乐潇, an Assistant Professor in the Department of Mathematics at the University of Hong Kong. My research is in nonconvex optimization, applied semialgebraic geometry, and data science. I received my Ph.D. degree from Columbia University in May 2024.

[Curriculum Vitae] [Google Scholar]

Email: Lai dot Lexiao at hku dot hk

Prospective Students: I am actively looking for a self-motivated Ph.D. student who is interested in the theory of optimization and data science. Ideal candidates will have a solid background in mathematics, with proficiency in programming being highly desirable. If you are interested in working with me, please email me your CV and transcripts.

Preprints and Publications

1. (with Cédric Josz and Xiaopeng Li) Proximal random reshuffling under local Lipschitz continuity, arXiv preprint, 2024 [preprint]
2. (with Cédric Josz) Sufficient conditions for instability of the subgradient method with constant step size, SIAM Journal on Optimization, 2024 [doi] [preprint]
3. (with Cédric Josz and Xiaopeng Li) Convergence of the momentum method for semialgebraic functions with locally Lipschitz gradients, SIAM Journal on Optimization, 2023 [doi] [preprint]
4. (with Cédric Josz) Global stability of first-order methods for coercive tame functions, Mathematical Programming, 2023 [doi] [preprint]
5. (with Cédric Josz) Lyapunov stability of the subgradient method with constant step size, Mathematical Programming, 2023 [doi] [preprint]
6. (with Cédric Josz) Nonsmooth rank-one matrix factorization landscape, Optimization Letters, 2021 [doi] [preprint]
7. (with Elliot Cartee, Qianli Song, and Alexander Vladimirsky) Time-dependent surveillance-evasion games, 58th IEEE Conference on Decision and Control, 2019 [website] [doi] [preprint]