Ling Liang

Ling Liang

Assistant Professor
Department of Mathematics, University of Tennessee, Knoxville

Research Interests

My research focuses on the development, analysis, and implementation of efficient, robust, and scalable algorithmic frameworks for solving large-scale optimization problems and their applications in machine learning, scientific computing, and engineering, aiming to bridge theoretical advancements with practical solutions.

  • Large-scale conic programming
  • Machine learning algorithms
  • Inexact optimization algorithms

Openings

I am looking for passionate and highly self-motivated graduate and undergraduate students to join our research group.

Research projects include optimization, machine learning and data science, and scientific computing. Students interested in large-scale optimization, mathematical foundations of machine learning, or scientific computing are especially encouraged to get in touch.

Please contact me by email with a brief description of your background and research interests.

Experience

  • Assistant Professor, Department of Mathematics, University of Tennessee, Knoxville, August 2025-present.
  • Postdoc, Department of Mathematics, University of Maryland, College Park, August 2023-July 2025. Host: Dr. Haizhao Yang.
  • Visiting Researcher, Weierstrass Institute for Applied Analysis and Stochastics, March 2023-June 2023. Host: Dr. Jia-Jie Zhu.
  • Research Fellow, Department of Mathematics, National University of Singapore, January 2022-July 2023. Host: Dr. Kim-Chuan Toh.

Education

  • Ph.D. in Mathematics, National University of Singapore, November 2021. Advisor: Dr. Kim-Chuan Toh.
  • B.S. in Mathematics, University of Science and Technology of China, June 2017. Advisor: Dr. Zhouwang Yang.

Preprints

  1. Ling Liang, Lei Yang. Mixed-precision GPU acceleration for large-scale minimum enclosing ball problems, 2026. arXiv.
  2. Ling Liang, Lei Yang. A provably convergent and practical algorithm for Gromov-Wasserstein optimal transport, 2026. arXiv.
  3. Di Wu, Ling Liang, Haizhao Yang. Beyond expected information gain: stable Bayesian optimal experimental design with integral probability metrics and plug-and-play extensions, 2026. arXiv.
  4. Lei Yang, Han Wan, Min Zhang, Ling Liang. Fast and effective computation of generalized symmetric matrix factorization, 2026. arXiv.
  5. Jiayi Zhu, Hong Wang, Ling Liang, Lei Yang. D-ripALM: A tuning-friendly decentralized relative-type inexact proximal augmented Lagrangian method, 2026. arXiv.
  6. Lei Yang, Jiayi Zhu, Ling Liang, Kim-Chuan Toh. Convergence of a relative-type inexact proximal ALM for convex nonlinear programming, 2025. arXiv.
  7. Raghav Thind, Youran Sun, Ling Liang, Haizhao Yang. OptimAI: Optimization from natural language using LLM-powered AI agents, 2025. arXiv.
  8. Rohan Bhatnagar, Ling Liang, Krish Patel, Haizhao Yang. From equations to insights: Unraveling symbolic structures in PDEs with LLMs, 2025. arXiv.
  9. Di Wu, Ling Liang, Haizhao Yang. PINS: Proximal iterations with sparse Newton and Sinkhorn for optimal transport, 2025. arXiv.
  10. Jiayi Zhu, Ling Liang, Lei Yang, and Kim-Chuan Toh. ripALM: A relative-type inexact proximal augmented Lagrangian method with applications to quadratically regularized optimal transport, 2024. arXiv.
  11. Ling Liang, Haizhao Yang. PNOD: An efficient projected Newton framework for exact optimal experimental designs, 2024. arXiv, code.
  12. Ling Liang, Cameron Austin, and Haizhao Yang. Accelerating multi-block constrained optimization through learning to optimize, 2024. arXiv.

Journal Publications

  1. Ling Liang, Kim-Chuan Toh, and Haizhao Yang. NewVEM: A Newton vertex exchange method for a class of constrained self-concordant minimization problems, Journal of Scientific Computing 105, no. 64 (2025). arXiv, JSC.
  2. Ling Liang, Qiyuan Pang, Kim-Chuan Toh, and Haizhao Yang. Nesterov's accelerated Jacobi-type methods for large-scale symmetric positive semidefinite linear systems, SIAM Journal on Scientific Computing 47, no. 6 (2025). arXiv, SISC, code.
  3. Ling Liang, Defeng Sun, and Kim-Chuan Toh. A squared smoothing Newton method for semidefinite programming. Mathematics of Operations Research 50, no. 4 (2025): 2433-3282. arXiv, MOOR.
  4. Ling Liang, Zusen Xu, Kim-Chuan Toh, and Jia-Jie Zhu. An inexact Halpern iteration with application to distributionally robust optimization, Journal of Optimization Theory and Applications 260, no. 58 (2025): 1-41. JOTA, arXiv, code.
  5. Ching-pei Lee, Ling Liang, Tianyun Tang, and Kim-Chuan Toh. Accelerating nuclear-norm regularized low-rank matrix optimization through Burer-Monteiro decomposition, Journal of Machine Learning Research 25, no. 379 (2024): 1-52. arXiv, JMLR, code.
  6. Ling Liang, Haizhao Yang. On the stochastic (variance-reduced) proximal gradient method for regularized expected reward optimization, Transactions on Machine Learning Research, 2024. arXiv, TMLR.
  7. Di Hou, Ling Liang, and Kim-Chuan Toh. A sparse smoothing Newton method for solving discrete optimal transport problems, ACM Transactions on Mathematical Software 50, no. 3 (2024): 1-26. arXiv, TOMS.
  8. Lei Yang, Ling Liang, Hong T.M. Chu, and Kim-Chuan Toh. A corrected inexact proximal augmented Lagrangian method with a relative error criterion for a class of group-quadratic regularized optimal transport problems. Journal of Scientific Computing 99, no. 79 (2024). arXiv, JSC.
  9. Hong T.M. Chu, Ling Liang, Kim-Chuan Toh, and Lei Yang. An efficient implementable inexact entropic proximal point algorithm for a class of linear programming problems. Computational Optimization and Applications 85, no. 1 (2023): 107-146. arXiv, COAP, code.
  10. Heng Yang, Ling Liang, Luca Carlone, and Kim-Chuan Toh. An inexact projected gradient method with rounding and lifting by nonlinear programming for solving rank-one semidefinite relaxation of polynomial optimization. Mathematical Programming 201, no. 1-2 (2023): 409-472. arXiv, MP, code.
  11. Ling Liang, Xudong Li, Defeng Sun, and Kim-Chuan Toh. QPPAL: A two-phase proximal augmented Lagrangian method for high dimensional convex quadratic programming problems. ACM Transactions on Mathematical Software 48, no. 3 (2022): 1-27. arXiv, TOMS, code.
  12. Ying Cui, Ling Liang, Defeng Sun, and Kim-Chuan Toh. On degenerate doubly nonnegative projection problems. Mathematics of Operations Research 47, no. 3 (2022): 2219-2239. arXiv, MOOR.
  13. Quoc Tran-Dinh, Ling Liang, and Kim-Chuan Toh. A new homotopy proximal variable-metric framework for composite convex minimization. Mathematics of Operations Research 47, no. 1 (2022): 508-539. arXiv, MOOR.
  14. Ling Liang, Defeng Sun, and Kim-Chuan Toh. An inexact augmented Lagrangian method for second-order cone programming with applications. SIAM Journal on Optimization 31, no. 3 (2021): 1748-1773. arXiv, SIOPT.

Conference Proceedings

  1. Shucheng Kang, Xiaoyang Xu, Jay Sarva, Ling Liang, and Heng Yang. Fast and certifiable trajectory optimization, in Algorithmic Foundations of Robotics XVI, Volume 1: Proceedings of the Sixteenth Workshop on the Algorithmic Foundations of Robotics, Springer Proceedings in Advanced Robotics, vol. 37, pp. 43-65, Springer, 2026. Springer, arXiv, code, Best Paper Award Finalist.

Teaching

  • Spring 2026, MATH251 Matrix Algebra I, Department of Mathematics, UTK.
  • Fall 2025, MATH519 Mathematical Methods of Machine Learning, Department of Mathematics, UTK.
  • Spring 2025, AMSC460 Computational Methods, Department of Mathematics, UMD.
  • Fall 2024, MATH241 Calculus III, Department of Mathematics, UMD.
  • Spring 2024, MATH401 Applications of Linear Algebra, Department of Mathematics, UMD.
  • Fall 2023, AMSC460 Computational Methods, Department of Mathematics, UMD.

Invited Talks

  • SIAM Conference on Mathematics of Data Science, Salt Lake City, November 2026. Upcoming
  • INFORMS Annual Meeting, San Francisco, November 2026. Upcoming
  • Numerical Analysis Seminar, UMD, September 2026. Upcoming
  • Modeling and Optimization: Theory and Applications, Lehigh University, August 2026. Upcoming
  • INFORMS Optimization Society Conference 2026, Atlanta, March 2026.
  • SIAM NNP Section Conference, Penn State, November 2025.
  • International Conference on Continuous Optimization, USC, Los Angeles, July 2025.
  • The 25th International Symposium on Mathematical Programming, Montreal, July 2024.
  • INFORMS Optimization Society Conference 2024, Rice University, March 2024.
  • Workshop of Scientific Machine Learning: Theory and Algorithms, UMD, February 2024.
  • SIAM Conference on Optimization, The Sheraton Grand Seattle, Seattle, May 2023.
  • HUA Loo-Keng Youth Forum in Applied Mathematics, AMSS, March 2023.
  • SIAM Conference on Optimization, Online, July 2021.
  • Workshop on Matrix Optimization, Beijing University of Technology, December 2019.
  • International Conference on Continuous Optimization, TU Berlin, August 2019.