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

Preprints

  1. Non-convex self-concordant functions: Practical algorithms and complexity analysis (with Donald Goldfarb, Tianyi Lin, and Jiayu Zhang), 2025 [preprint]
  2. On the diameter of subgradient sequences in o-minimal structures (with Mingzhi Song), 2025 [preprint]
  3. Proximal random reshuffling under local Lipschitz continuity (with Cédric Josz and Xiaopeng Li), 2024 [preprint]

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]