About me

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. Currently, I am interested in

• Semidefinite Programming
• Computational Optimal Transport
• Machine Learning Algorithms
• Inexact Optimization Algorithms

Experience

• Postdoctoral Associate (August 2023 - present)
  • University of Maryland, College Park
  • Host: Dr. Haizhao Yang
• Visiting Researcher (March 2023 - June 2023)
  • Weierstrass Institute for Applied Analysis and Stochastics
  • Host: Dr. Jia-Jie Zhu
• Research Fellow (January 2022 - July 2023)
  • National University of Singapore
  • Host: Dr. Kim-Chuan Toh

Education

• Ph.D. in Mathematics (August 2017 - November 2021)
  • National University of Singapore
  • Honorably supervised by Dr. Kim-Chuan Toh
• B.S. in Mathematics (September 2013 - June 2017)
  • University of Science and Technology of China

Papers

Preprints

1. Rohan Bhatnagar, Ling Liang, Krish Patel, Haizhao Yang. From equations to insights: unraveling symbolic structures in PDEs with LLMs, 2025. arXiv
2. Di Wu, Ling Liang, Haizhao Yang. PINS: Proximal iterations with sparse Newton and Sinkhorn for optimal transport, 2025. arXiv
3. 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
4. Ling Liang, Haizhao Yang. PNOD: An efficient projected Newton framework for exact optimal experimental designs, 2024. arXiv, CODE
5. Ling Liang, Cameron Austin, and Haizhao Yang. Accelerating multi-block constrained optimization through learning to optimize, 2024. arXiv
6. Ling Liang, Kim-Chuan Toh, and Haizhao Yang. Vertex exchange method for a class of convex quadratic programming problems, 2024. arXiv
7. Ling Liang, Qiyuan Pang, Kim-Chuan Toh, and Haizhao Yang. Nesterov’s accelerated Jacobi-type methods for large-scale symmetric positive semidefinite linear systems, 2024. arXiv
8. Ling Liang, Kim-Chuan Toh, and Jia-Jie Zhu. An inexact Halpern iteration with application to distributionally robust optimization, 2024. arXiv, CODE

Journal Publications

1. 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
2. Ling Liang, Defeng Sun, and Kim-Chuan Toh. A squared smoothing Newton method for semidefinite programming. Mathematics of Operations Research, 2024. arXiv MOOR
3. 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
4. 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
5. 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
6. 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
7. 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
8. 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
9. 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
10. 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
11. 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, Workshop on the Algorithmic Foundations of Robotics, 2024. arXiv, CODE

Ph.D. Dissertation

Augmented Lagrangian Methods for A Class of Large-Scale Conic Programming, 2021.

Invited Talks

• The 25th International Symposium on Mathematical Programming, Montreal, July 2024
• 2024 INFORMS Optimization Society Conference, 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 Luogeng 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
• The Sixth International Conference on Continuous Optimization, TU Berlin, August 2019

Teaching

• 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

Services

Review

• Mathematical Programming
• SIAM Journal on Optimization
• Mathematical Programming Computation
• SIAM Journal on Mathematics of Data Science
• Computational Optimization and Applications
• Journal of Scientific Computing
• INFORMS Journal on Computing
• Optimization Methods and Software
• Journal of Industrial and Management Optimization
• Asia-Pacific Journal of Operational Research
• Transactions on Machine Learning Research

Organization

• Organizer, Summer School on Scientific Machine Learning, UMD (Summer 2025)
• Session Chair, International Conference on Continuous Optimization, USC (Summer 2025)
• Organizer, Numerical Analysis Seminar, UMD (Fall 2024 - Spring 2025)
• Session Chair, Optimization in the Big Data Era, NUS (Winter 2022)