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.

[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. Nonsmooth rank-one symmetric matrix factorization landscape (with Cédric Josz), Optimization Letters, 2025 [journal] [preprint]
  2. Sufficient conditions for instability of the subgradient method with constant step size (with Cédric Josz), SIAM Journal on Optimization, 2024 [journal] [preprint]
  3. 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]
  4. Global stability of first-order methods for coercive tame functions (with Cédric Josz), Mathematical Programming, 2023 [journal] [preprint]
  5. Lyapunov stability of the subgradient method with constant step size (with Cédric Josz), Mathematical Programming, 2023 [journal] [preprint]
  6. Nonsmooth rank-one matrix factorization landscape (with Cédric Josz), Optimization Letters, 2021 [journal] [preprint]
  7. Time-dependent surveillance-evasion games (with Elliot Cartee, Qianli Song, and Alexander Vladimirsky), 58th IEEE Conference on Decision and Control, 2019 [website] [proceeding] [preprint]

Preprints

  1. Phase transitions in phase-only compressed sensing (with Junren Chen and Arian Maleki), 2025 [preprint]
  2. Proximal random reshuffling under local Lipschitz continuity (with Cédric Josz and Xiaopeng Li), 2024 [preprint]