Optimization · Machine learning · Power systems

Richard Y. Zhang

Associate Professor
Department of Electrical and Computer Engineering
Coordinated Science Laboratory
University of Illinois Urbana-Champaign
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My research focuses on low-rank optimization, both as a theoretical lens for understanding how learning algorithms uncover latent signals from complex data, and also as a computational framework for designing large-scale algorithms by operating on these signals.

I received my PhD from MIT EECS and was a postdoc at Berkeley IEOR. I received an NSF CAREER Award in 2021 and have served as an Area Chair at NeurIPS, ICML, and ICLR. I am advising PhD students Hong-Ming Chiu, Iven Guzel, Jing-Teng (Jeter) Hwang, and Haoruo Zhang; Masters student Nalin Tiwary; Undergraduate Kevin Wu. Alumni from my group include Gavin (Jialun) Zhang (PhD '24 → Meta), and June Hou (MS '25 → UIUC PhD).

In Fall 2026, I am teaching ECE490: Introduction to Optimization.

Richard Y. Zhang

Publications

  • Sharp Recovery and Landscape Guarantees for the Nonconvex Matrix LASSO
    A.D. McRae, R. Y. Zhang — Preprint, Apr 2026. [arxiv]
  • Sharp Global Guarantees for Nonconvex Low-Rank Recovery in the Noisy Overparameterized Regime
    R. Y. Zhang — SIAM Journal on Optimization, 35.3 (2025): pp. 2128-2154. [doi] [arxiv]
  • Preconditioned Gradient Descent for Overparameterized Nonconvex Burer-Monteiro Factorization with Global Optimality Certification
    G. Zhang, S. Fattahi, R.Y. Zhang — Journal of Machine Learning Research, 24.163 (2023): pp. 1-55. [permalink] [arxiv]
  • Statistically Optimal K-means Clustering via Nonnegative Low-rank Semidefinite Programming
    Selected for Oral (one of 85/7262 submissions)
    Y. Zhuang, X. Chen, Y. Yang, R.Y. Zhang — ICLR 2024. [arxiv]
  • SDP-CROWN: Efficient Bound Propagation for Neural Network Verification with Tightness of Semidefinite Programming
    Selected for Spotlight (one of 313/12107 submissions)
    Hong-Ming Chiu, Hao Chen, Huan Zhang, Richard Y. Zhang — ICML 2025. [arxiv]
  • Power System State Estimation by Phase Synchronization and Eigenvectors
    I. Guzel, R. Y. Zhang — IEEE Transactions on Control of Network Systems, 12.3 (2025): pp. 2207-2218. [doi] [arxiv]
Preprints
  • Sharp Recovery and Landscape Guarantees for the Nonconvex Matrix LASSO
    A.D. McRae, R. Y. Zhang — Preprint, Apr 2026. [arxiv]
  • Well-conditioned Primal-Dual Interior-point Method for Low-rank Semidefinite Programming
    H.-M. Chiu, R. Y. Zhang — Preprint, Jul 2024. [arxiv]
  • Spectral Initialization and Certification for Power System Angle Estimation
    I. Guzel, A.D. McRae, R. Y. Zhang — Preprint, Jul 2026. [arxiv]
2026
  • Nonnegative Low-rank Matrix Recovery Can Have Spurious Local Minima
    R. Y. Zhang — Optimization Letters, 20 (2026): pp. 683-704. [doi] [arxiv]
  • Scalable Second-order Riemannian Optimization for K-means Clustering
    Peng Xu*, Chun Ying Hou*, Xiaohui Chen, Richard Y. Zhang — ICLR 2026. [arxiv]
2025
  • Sharp Global Guarantees for Nonconvex Low-Rank Recovery in the Noisy Overparameterized Regime
    R. Y. Zhang — SIAM Journal on Optimization, 35.3 (2025): pp. 2128-2154. [doi] [arxiv]
  • Improved Global Guarantees for the Nonconvex Burer--Monteiro Factorization via Rank Overparameterization
    R. Y. Zhang — Mathematical Programming, 213 (2025): pp. 1009-1038. [doi] [arxiv]
  • Complexity of Sparse Semidefinite Programs with Small Treewidth
    R. Y. Zhang — Mathematical Programming, 213 (2025): pp. 201-237. [doi] [arxiv]
  • Simple Alternating Minimization Provably Solves Complete Dictionary Learning
    G. Liang, G. Zhang, S. Fattahi, R.Y. Zhang — SIAM Journal on Mathematics of Data Science, 7.3 (2025): pp. 855-883. [doi] [arxiv]
  • Power System State Estimation by Phase Synchronization and Eigenvectors
    I. Guzel, R. Y. Zhang — IEEE Transactions on Control of Network Systems, 12.3 (2025): pp. 2207-2218. [doi] [arxiv]
  • SDP-CROWN: Efficient Bound Propagation for Neural Network Verification with Tightness of Semidefinite Programming
    Selected for Spotlight (one of 313/12107 submissions)
    Hong-Ming Chiu, Hao Chen, Huan Zhang, Richard Y. Zhang — ICML 2025. [arxiv]
2024
  • Statistically Optimal K-means Clustering via Nonnegative Low-rank Semidefinite Programming
    Selected for Oral (one of 85/7262 submissions)
    Y. Zhuang, X. Chen, Y. Yang, R.Y. Zhang — ICLR 2024. [arxiv]
  • Fast and Minimax Optimal Estimation of Low-Rank Matrices via Non-Convex Gradient Descent
    G. Zhang, H.-M. Chiu, R.Y. Zhang — AISTATS 2024. [arxiv]
2023
  • Preconditioned Gradient Descent for Overparameterized Nonconvex Burer-Monteiro Factorization with Global Optimality Certification
    G. Zhang, S. Fattahi, R.Y. Zhang — Journal of Machine Learning Research, 24.163 (2023): pp. 1-55. [permalink] [arxiv]
  • Tight Certification of Adversarially Trained Neural Networks via Nonconvex Low-Rank Semidefinite Relaxations
    H.-M. Chiu, R.Y. Zhang — ICML 2023. [arxiv]
2022
  • Accelerating SGD for Highly Ill-Conditioned Huge-Scale Online Matrix Completion
    G. Zhang, H.-M. Chiu, R.Y. Zhang — NeurIPS 2022. [arxiv]
2021
  • Sparse Semidefinite Programs with Guaranteed Near-Linear Time Complexity via Dualized Clique Tree Conversion
    R.Y. Zhang, J. Lavaei — Mathematical Programming, 188.1 (2021): pp. 351-393. [doi] [arxiv]
  • Uniqueness of Power Flow Solutions Using Monotonicity and Network Topology
    S.-W. Park, R.Y. Zhang, J. Lavaei, R. Baldick — IEEE Transactions on Control of Network Systems, 8.1 (2021): pp. 319-330. [doi]
  • Preconditioned Gradient Descent for Over-Parameterized Nonconvex Matrix Factorization
    G. Zhang, S. Fattahi, R.Y. Zhang — NeurIPS 2021. [permalink]
2020
  • Large-Scale Traffic Signal Offset Optimization
    Y. Ouyang, R.Y. Zhang, J. Lavaei, P. Varaiya — IEEE Transactions on Control of Network Systems, 7.3 (2020): pp. 1176-1187. [arxiv] [pdf]
  • How many samples is a good initial point worth in Low-rank Matrix Recovery?
    Selected for Spotlight (one of 280/9454 submissions)
    G. Zhang, R.Y. Zhang — NeurIPS 2020. [arxiv]
  • On the Tightness of Semidefinite Relaxations for Certifying Robustness to Adversarial Examples
    R.Y. Zhang — NeurIPS 2020. [arxiv]
2019
  • Sharp Restricted Isometry Bounds for the Inexistence of Spurious Local Minima in Nonconvex Matrix Recovery
    R.Y. Zhang, S. Sojoudi, J. Lavaei — Journal of Machine Learning Research, 20.114 (2019): pp. 1-34. [permalink] [arxiv]
  • Spurious Local Minima in Power System State Estimation
    Special Issue on Analysis, Control and Optimization of Energy System Networks
    R.Y. Zhang, J. Lavaei, R. Baldick — IEEE Transactions on Control of Network Systems, 6.3 (2019): pp. 1086-1096. [doi] [pdf]
  • Conic optimization for control, energy systems, and machine learning: Applications and algorithms
    R.Y. Zhang, C. Josz, S. Sojoudi — Annual Reviews in Control, 47 (2019): pp. 323-340. [doi] [arxiv]
  • Monotonicity Between Phase Angles and Power Flow and Its Implications for the Uniqueness of Solutions
    S.W. Park, R.Y. Zhang, J. Lavaei, R. Baldick — HICSS 52.
2018
  • GMRES-Accelerated ADMM for Quadratic Objectives
    R.Y. Zhang, J.K. White — SIAM Journal on Optimization, 28.4 (2018): pp. 3025-3056. [doi] [arxiv]
  • How Much Restricted Isometry is Needed In Nonconvex Matrix Recovery?
    Selected for Spotlight (one of 168/4856 submissions)
    R.Y. Zhang, C. Josz, S. Sojoudi, J. Lavaei — NeurIPS 2018. [arxiv]
  • Large-Scale Sparse Inverse Covariance Estimation via Thresholding and Max-Det Matrix Completion
    R.Y. Zhang, S. Fattahi, S. Soujoudi — ICML 2018. [permalink] [arxiv] [slides]
  • A theory on the absence of spurious solutions for nonconvex and nonsmooth optimization
    C. Josz, Y. Ouyang, R. Y. Zhang, J. Lavaei, S. Sojoudi — NeurIPS 2018. [arxiv]
  • Sparse Semidefinite Programs with Near-Linear Time Complexity
    R.Y. Zhang, J. Lavaei — CDC 2018. [arxiv]
  • Efficient Algorithm for Large-and-Sparse LMI Feasibility Problems
    R.Y. Zhang, J. Lavaei — CDC 2018. [pdf]
  • Conic Approximation with Provable Guarantee for Traffic Signal Offset Optimization
    Y. Ouyang, R.Y. Zhang, J. Lavaei, P. Varaiya — CDC 2018. [pdf]
  • Sparse Inverse Covariance Estimation for Chordal Structures
    S. Fattahi, R.Y. Zhang, S. Sojoudi — ECC 2018. [arxiv]
  • Conic Optimization Theory: Convexification Techniques and Numerical Algorithms
    R.Y. Zhang*, C. Josz*, S. Sojoudi — ACC 2018. [doi] [arxiv]
  • Spurious Critical Points in Power System State Estimation
    R.Y. Zhang, J. Lavaei, R. Baldick — HICSS 51. [doi] [pdf]
  • Linear Time Algorithms for Sparse Inverse Covariance Estimation
    S. Fattahi, R. Y. Zhang, S. Sojoudi — IEEE Access, 7 (2018): pp. 12658-12672. [doi]
2017
  • Modified Interior-Point Method for Large-and-Sparse Low-Rank Semidefinite Programs
    R.Y. Zhang, J. Lavaei — CDC 2017. [doi] [arxiv]
2016
  • Robust Stability Analysis for Large-Scale Power Systems
    R.Y. Zhang — Ph.D. thesis, MIT Department of Electrical Engineering & Computer Science, 2016. [permalink] [pdf]
  • Certifying Microgrid Stability Under Large-Signal Intermittency
    R.Y. Zhang, J. Elizondo, J.L. Kirtley, J.K. White — COMPEL 2016. [doi]
  • Small-Signal Stability Verification Issues for Transmission Systems with Distributed Renewables
    R.Y. Zhang, J. Elizondo, J.L. Kirtley, J.K. White — PESGM 2016. [doi] [pdf]
  • Inertial and Frequency Response from Microgrids with Induction Motors
    J. Elizondo, R.Y. Zhang, P.-H. Huang, J.K. White, J.L. Kirtley — COMPEL 2016. [doi]
  • Parameter Insensitivity in ADMM-Preconditioned Solution of Saddle-Point Problems
    R.Y. Zhang, J.K. White — Tech report, Feb 2016. [arxiv]
2015
  • Toeplitz-Plus-Hankel Matrix Recovery for Green’s Function Computations on General Substrates
    R.Y. Zhang, J.K. White — Proceedings of the IEEE, 103.11 (2015): pp. 1970-1984. [doi] [pdf]
  • Design of Resonance Damping via Control Synthesis
    R.Y. Zhang, A.-T. Avestruz, J.K. White, S.B. Leeb — COMPEL 2015. [doi] [pdf]
  • Robust Small Signal Stability for Microgrids under Uncertainty
    J. Elizondo, R.Y. Zhang, J.K. White, J.L. Kirtley — PEDG 2015. [doi] [pdf]
  • An energy-based method for the assessment of battery and ultracapacitor in pulse load applications
    Outstanding Presentation Award (Poster)
    Y. He, R.Y. Zhang, J.G. Kassakian — APEC 2015. [doi] [pdf]
2014
  • Fast simulation of complicated 3D structures above lossy magnetic media
    R.Y. Zhang, J.K. White, J.G. Kassakian — IEEE Transactions on Magnetics, 50.10 (2014): 7027416. [doi] [pdf]
  • Analytical model for effects of twisting on litz-wire losses
    C.R. Sullivan, R.Y. Zhang — COMPEL 2014. [doi] [pdf]
  • Realistic litz wire characterization using fast numerical simulations
    Outstanding Presentation Award (Oral)
    R.Y. Zhang, J.K. White, J.G. Kassakian, C.R. Sullivan — APEC 2014. [doi] [pdf] [slides]
  • Simplified design method for litz wire
    C.R. Sullivan, R.Y. Zhang — APEC 2014. [doi] [pdf]
2011-2013
  • A Generalized Approach to Planar Induction Heating Magnetics
    R.Y. Zhang — S.M. thesis, MIT Department of Electrical Engineering & Computer Science, 2012. [permalink] [pdf]
  • The Future of the Electric Grid -- An Interdisciplinary MIT study
    J.G. Kassakian, R. Schmalensee et al. — Technical report, MIT Energy Initiative, 2011. [permalink]
2010
  • A go-cart as an electric vehicle for undergraduate teaching and assessment
    B. Heffernan, R. Duke, R. Zhang, P. Gaynor, M. Cusdin — AUPEC 2010.

Software

Soft-Thresholding and Max-Det Matrix Completion for Graphical Lasso

In our ICML 2018 paper, we describe an algorithm that recovers the graphical lasso estimator of Friedman et al. (2008) in O(n²/p + n) time over p parallel processors. Given the sample matrix X = [x₁, …, xN], we first compute the soft-thresholded sample covariance matrix Cλ in O(n²/p) time and O(n·N) memory. Then, we solve an associated maximum determinant matrix completion problem using Cλ as input in O(n) time and memory.

[github][Associated paper]
Modified SeDuMi

A modified version of SeDuMi with identical syntax for large-and-sparse low-rank semidefinite programs. If the n × n solution matrix is low-rank and if the problem data is "sufficiently sparse", then each SeDuMi iteration costs O(n³) time and O(n²) memory. Lorentz cone is not (yet) supported.

[github][Associated paper]
fastlitz - Realistic litz wire characterization

Simulates litz wires in three-dimensions using the PEEC formulation. Computes the resistance of a wire, and the induced eddy loss when exposed to a magnetic field. Comes with a nice graphical user interface. UPDATE 04/14: Removed dependencies on MATLAB Statistics Toolbox.

[github][Associated paper]

Trivia

My last name 张/張 (Zhāng) is pronounced “Dj-uh-ng”, but I usually go by the anglicized “Z-ang.” People often confuse me with Dr. Richard Zhang, which is why I usually state my middle initial. I am originally from New Zealand. I was in a post-rock band in college.