**Assistant Professor**

Department of Electrical and Computer Engineering

Coordinated Science Laboratory

University of Illinois at Urbana-Champaign

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My research is in optimization and machine learning, and their applications in power and energy systems. Specifically: Nonconvex optimization (low-rank matrix factorization); Convex optimization (semidefinite programming); Large-scale linear systems (Krylov subspaces); Exploiting domain-specific structure (small treewidth, quadratic nonconvexity, monotonicity) to solve problems in power and energy with *provable guarantees* on quality, speed, and safety.

I received my PhD in Electrical Engineering and Computer Science from MIT in 2017, and was a postdoc at UC Berkeley from 2017-2019.

**April 2021.**New preprint makes sharp global guarantees for nonconvex low-rank matrix recovery in which the search rank is allowed to exceed the true rank: Sharp Global Guarantees for Nonconvex Low-Rank Matrix Recovery in the Overparameterized Regime.**January 2021.**Delighted and honored to receive the NSF CAREER Award.**September 2020.**Two papers accepted at__NeuIPS 2020__:**(Spotlight)**How Many Samples is a Good Initial Point Worth in Low-rank Matrix Recovery? and**(Poster)**On the Tightness of Semidefinite Relaxations for Certifying Robustness to Adversarial Examples.**June 2020.**New preprint shows that the SDP relaxation of ReLU networks is generally tight for a single hidden layer and generally loose for multiple layers: On the Tightness of Semidefinite Relaxations for Certifying Robustness to Adversarial Examples.**June 2020.**New preprint quantifies the value of a good initial point for nonconvex matrix recovery: How Many Samples is a Good Initial Point Worth?**April 2020.**Paper on solving sparse semidefinite programs in near-linear time to appear in__Mathematical Programming__: Sparse Semidefinite Programs with Guaranteed Near-Linear Time Complexity via Dualized Clique Tree Conversion.**November 2019.**Paper on optimizing the relative timing of traffic signals to appear in the__IEEE Transactions on Control of Network Systems__: Large-Scale Traffic Signal Offset Optimization.**June 2019.**Paper on the Restricted Isometry Property (RIP) for nonconvex matrix recovery problem to appear in the__Journal of Machine Learning Research (JMLR)__: Sharp Restricted Isometry Bounds for the Inexistence of Spurious Local Minima in Nonconvex Matrix Recovery.**May 2019.**I will be joining ECE Illinois (UIUC) as an Assistant Professor starting August 2019.**May 2019.**Paper on the nonconvex power system state estimation problem to appear in a special issue of__IEEE Transactions on Control of Network Systems__: Spurious Local Minima in Power System Estimation.**January 2019.**New preprint proves that the (2,1/2)-Restricted Isometry Property (RIP) is both necessary and sufficient for the rank-1 nonconvex matrix recovery problem to contain no spurious local minima: Sharp Restricted Isometry Bounds for the Inexistence of Spurious Local Minima in Nonconvex Matrix Recovery.**December 2018.**Presented 2 papers at__NeurIPS 2018__: (Spotlight) (Poster) How Much Restricted Isometry is Needed In Nonconvex Matrix Recovery? (Poster) A Theory on the Absence of Spurious Solutions for Nonconvex and Nonsmooth Optimization. (Of 4856 total submissions, 1011 were accepted, including 30 orals and 168 spotlights.)**October 2018.**Paper on accelerating ADMM using Krylov subspace appeared in__SIAM Journal on Optimization__: GMRES-Accelerated ADMM for Quadratic Objectives.

**How Much Restricted Isometry is Needed In Nonconvex Matrix Recovery?***NeurIPS 2018 Spotlight (5 min)*

[paper] [slides] [poster]

Recommendation engines (think YouTube and Netflix) frequently make use of low-rank matrix models. In practice, these are easily trained using SGD, apparently without getting stuck at a local minimum. In this paper, we show that we've just been getting lucky—SGD is readily defeated by bad models that "look easy" to train.

**Large-Scale Sparse Inverse Covariance Estimation via Thresholding and Max-Det Matrix Completion***ICML 2018 (10 min)*

[paper] [slides] [poster]

Graphical lasso is able to estimate a graphical model on \(n\) vertices from \(O(n\log(n))\) data points. We describe an algorithm that solves graphical lasso in linear \(O(n)\) time and memory, thereby allowing extremely large graphical models to be learned on laptop computers.

**Sharp Global Guarantees for Nonconvex Low-Rank Matrix Recovery in the Overparameterized Regime?**

R.Y. Zhang - Preprint, 2021. [arxiv]**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 2020Advances in Neural Information Processing Systems. [arxiv]**On the Tightness of Semidefinite Relaxations for Certifying Robustness to Adversarial Examples**

R.Y. Zhang -NeurIPS 2020Advances in Neural Information Processing Systems. [arxiv]**Sparse Semidefinite Programs with Guaranteed Near-Linear Time Complexity via Dualized Clique Tree Conversion**

R.Y. Zhang, J. Lavaei -*Mathematical Programming*, 2020. [doi][arxiv]**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]**GMRES-Accelerated ADMM for Quadratic Objectives**

R.Y. Zhang, J.K. White -*SIAM Journal on Optimization*, 28.4 (2018): pp. 3025-3056. [doi] [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*, 2019. [doi][pdf]**Large-Scale Traffic Signal Offset Optimization**

Y. Ouyang, R.Y. Zhang, J. Lavaei, P. Varaiya -*IEEE Transactions on Control of Network Systems*, 2019. [doi][arxiv]

**Sharp Global Guarantees for Nonconvex Low-Rank Matrix Recovery in the Overparameterized Regime?**

R.Y. Zhang - Preprint, 2021. [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*, 2021. [doi]

**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 2020Advances in Neural Information Processing Systems. [arxiv]**On the Tightness of Semidefinite Relaxations for Certifying Robustness to Adversarial Examples**

R.Y. Zhang -NeurIPS 2020Advances in Neural Information Processing Systems. [arxiv]**Sparse Semidefinite Programs with Guaranteed Near-Linear Time Complexity via Dualized Clique Tree Conversion**

R.Y. Zhang, J. Lavaei -*Mathematical Programming*, 2020. [doi][arxiv]

**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*, 2019. [doi][pdf]**Large-Scale Traffic Signal Offset Optimization**

Y. Ouyang, R.Y. Zhang, J. Lavaei, P. Varaiya -*IEEE Transactions on Control of Network Systems*, 2019. [doi][arxiv]**Conic Optimization With Applications to Machine Learning and Energy Systems**

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 52Hawaii International Conference on System Sciences.

**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 2018Advances in Neural Information Processing Systems. [arxiv]**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 2018Advances in Neural Information Processing Systems. [arxiv]**Large-Scale Sparse Inverse Covariance Estimation via Thresholding and Max-Det Matrix Completion**

R.Y. Zhang, S. Fattahi, S. Soujoudi -ICML 2018International Conference on Machine Learning. [permalink] [arxiv] [slides]**Sparse Semidefinite Programs with Near-Linear Time Complexity**

R.Y. Zhang, J. Lavaei -CDC 201857th IEEE Conference on Decision and Control. [arxiv]**Efficient Algorithm for Large-and-Sparse LMI Feasibility Problems**

R.Y. Zhang, J. Lavaei -CDC 201857th IEEE Conference on Decision and Control. [pdf]**Conic Approximation with Provable Guarantee for Traffic Signal Offset Optimization**

Y. Ouyang, R.Y. Zhang, J. Lavaei, P. Varaiya -CDC 201857th IEEE Conference on Decision and Control. [pdf]**Sparse Inverse Covariance Estimation for Chordal Structures**

S. Fattahi, R.Y. Zhang, S. Sojoudi -ECC 2018European Control Conference 2018. [arxiv]**Spurious Critical Points in Power System State Estimation**

R.Y. Zhang, J. Lavaei, R. Baldick -HICSS 51Hawaii International Conference on System Sciences. [doi] [pdf]**Conic Optimization Theory: Convexification Techniques and Numerical Algorithms**

R.Y. Zhang*, C. Josz*, S. Sojoudi -ACC 2018American Control Conference. [doi] [arxiv]

**Modified Interior-Point Method for Large-and-Sparse Low-Rank Semidefinite Programs**

R.Y. Zhang, J. Lavaei -CDC 201756th IEEE Conference on Decision and Control. [doi] [arxiv]

**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 2016Seventeenth IEEE Workshop on Control and Modeling for Power Electronics. [doi]**Inertial and Frequency Response from Microgrids with Induction Motors**

J. Elizondo, R.Y. Zhang, P.-H. Huang, J.K. White, J.L. Kirtley -COMPEL 2016Seventeenth IEEE Workshop on Control and Modeling for Power Electronics. [doi]**Small-Signal Stability Verification Issues for Transmission Systems with Distributed Renewables**

R.Y. Zhang, J. Elizondo, J.L. Kirtley, J.K. White -PESGM 2016IEEE Power & Energy Society General Meeting 2016. [doi] [pdf]**Parameter Insensitivity in ADMM-Preconditioned Solution of Saddle-Point Problems**

R.Y. Zhang, J.K. White - Feb 2016. [arxiv]

**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 2015Sixteenth IEEE Workshop on Control and Modeling for Power Electronics. [doi] [pdf]**Robust Small Signal Stability for Microgrids under Uncertainty**

J. Elizondo, R.Y. Zhang, J.K. White, J.L. Kirtley -PEDG 20156th International Symposium on Power Electronics for Distributed Generation Systems. [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 2015IEEE Applied Power Electronics Conference and Exposition 2015. [doi] [pdf]

**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 2014Fifteenth IEEE Workshop on Control and Modeling for Power Electronics. [doi] [pdf]**Characterization of realistic litz wires using fast simulations***Outstanding Presentation Award (Oral)*

R.Y. Zhang, J.K. White, J.G. Kassakian, C.R. Sullivan -APEC 2014IEEE Applied Power Electronics Conference and Exposition 2014. [doi] [pdf] [slides]**Simplified design method for litz wire**

C.R. Sullivan, R.Y. Zhang -APEC 2014IEEE Applied Power Electronics Conference and Exposition 2014. [doi] [pdf]

**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, G. Desgroseilliers, T.D. Heidel, K. Afridi, A.M. Farid, J.M. Grochow, W.W. Hogan, H.D. Jacoby, J.L. Kirtley, H.G. Michaels, I. Perez-Arriaga, D.J. Perreault, N.L. Rose, G. Wilson, N. Abudaldah, M. Chen, P.E. Donohoo, S.J. Gunter, P.J. Kwok, V.A. Sakhrani, J. Wang, A. Whitaker, X.L. Yap, R.Y. Zhang - MIT Energy Initiative, 2011. [permalink]

I am a New Zealander of Chinese descent from Christchurch, New Zealand. My last name 张/張 (Zhāng) is pronounced "Dj-uh-ng", but I usually go by the anglicized "Z-ang". 我会说普通话。J'ai étudié le français à l'école. I was a guitarist in the post-rock band Mammoth (see Two Weeks and Life without Light).

People often confuse me with the computer vision expert formerly at Berkeley, or the MIT grad student who co-founded FAIL!, or the power electronics expert at GE, which is why I usually give my middle initial when stating my name. But even then, my name still collides with the researcher at Pfizer and the optometrist in Lexington, MA.

© 2018 Richard Y. Zhang.