Lexiao Lai

Lexiao Lai

Assistant Professor at HKU Math

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. I am advising PhD students Mingzhi Song and Kaiwei Yang.

[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 starting in Fall 2026, who is interested in the theory of optimization and/or 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.

Publications

  1. Phase transitions in phase-only compressed sensing (with Junren Chen and Arian Maleki), IEEE International Symposium on Information Theory (ISIT), 2025 [proceeding] [preprint]
  2. Nonsmooth rank-one symmetric matrix factorization landscape (with Cédric Josz), Optimization Letters, 2025 [journal] [preprint]
  3. Sufficient conditions for instability of the subgradient method with constant step size (with Cédric Josz), SIAM Journal on Optimization, 2024 [journal] [preprint]
  4. Convergence of the momentum method for semialgebraic functions with locally Lipschitz gradients (with Cédric Josz and Xiaopeng Li), SIAM Journal on Optimization, 2023 [journal] [preprint]
  5. Global stability of first-order methods for coercive tame functions (with Cédric Josz), Mathematical Programming, 2023 [journal] [preprint]
  6. Lyapunov stability of the subgradient method with constant step size (with Cédric Josz), Mathematical Programming, 2023 [journal] [preprint]
  7. Nonsmooth rank-one matrix factorization landscape (with Cédric Josz), Optimization Letters, 2021 [journal] [preprint]
  8. Time-dependent surveillance-evasion games (with Elliot Cartee, Qianli Song, and Alexander Vladimirsky), IEEE Conference on Decision and Control (CDC), 2019 [website] [proceeding] [preprint]

Preprints

  1. Proximal random reshuffling under local Lipschitz continuity (with Cédric Josz and Xiaopeng Li), 2024 [preprint]