My research interests sit around numerical analysis, optimization, and algorithms for scientific computing.
Research Interests
- Numerical analysis
- PDE-constrained optimization algorithms
- Parallel-in-time methods
- Recurrent neural networks
- Embedded nonlinear optimization
Earlier Projects
Wind power forecasting for wind farms
Advisors: Zaiwen Wen, Pingwen Zhang
Structured linearization and algorithms for gyroscopic and palindromic eigenvalue problems
Advisor: Yunfeng Cai
Thesis
Parareal-Based Preconditioners for Linear-Quadratic Optimal Control Problems
Advisor: Matthias Heinkenschloss
Reading Group
I co-organized a reading group discussing problems across applied mathematics, with topics ranging from numerical analysis to optimization and operations research. The group stopped during the COVID-19 pandemic.
Members and Guest Speaker
- Honglin Yuan, Stanford Ph.D., currently at Citadel
- Shengchao Lin, Rice Ph.D., currently at MathWorks
- Luze Xu, University of Michigan Ph.D., currently at UC Davis
- Xiaoyi Gu, Georgia Institute of Technology Ph.D., currently at Susquehanna International Group
- Yaqi Duan, Princeton Ph.D., currently at MIT
- Dawei Li, UIUC Ph.D., currently at U Chicago
- Guest speaker: Kailai Xu, Stanford Ph.D., currently at Citadel
Reading group presentation archive
- May 06, 2018: On the Local Minima Free Condition of Backpropagation Learning, Dawei Li
- May 14, 2018: Exact Augmented Lagrangian Duality for Mixed Integer Programming, Xiaoyi Gu
- May 30, 2018: Introduction to Implicit Constraint Optimization, Shengchao Lin
- Jun 21, 2018: More Virtuous Smoothing, Luze Xu
- Jul 23, 2018: Adaptive Low-Rank Approximation for State Aggregation of Markov Chain, Yaqi Duan
- Aug 07, 2018: Exact Augmented Lagrangian Duality for Mixed Integer Programming Ver.2, Xiaoyi Gu
- Aug 15, 2018: Introduction to Parareal algorithm, Shengchao Lin
- Oct 27, 2018: Total Unimodular Matrix, Luze Xu
- Nov 10, 2018: Temporal Difference Learning and A Finite Time Analysis with Linear Approximation, Dawei Li
- Dec 02, 2018: Acceleration Theory: Convex and Nonconvex (Part I), Honglin Yuan
- Dec 16, 2018: Over-Parameterized Deep Neural Networks Have No Strict Local Minima For Any Continuous Activations, Dawei Li
- Jan 26, 2019: State Aggregation Learning From Markov Transition Data, Yaqi Duan
- Apr 07, 2019: On Proximity For Pure Integer Linear Optimization, Luze Xu
- Jun 16, 2019: Adversarial Numerical Analysis, Kailai Xu
- Jun 27, 2019: Parareal-Based Preconditioners for Linear-Quadratic Optimal Control Problems, Shengchao Lin
- Nov 21, 2019: Sub-Optimal Local Minima Exist for Almost All Over-parameterized Neural Networks, Dawei Li
- Jun 25, 2020: Improving proximity bounds using sparsity, Luze Xu