21 citations · 103 across the 11 of their papers we have counts for
12 papers
On the Tightness of Semidefinite Relaxations for Certifying Robustness to Adversarial Examples
Richard Y. Zhang
The robustness of a neural network to adversarial examples can be provably certified by solving a convex relaxation. If the relaxation is loose, however, then the resulting certifi…
Large-Scale Traffic Signal Offset Optimization
Yi Ouyang, Richard Y. Zhang, Javad Lavaei +1
The offset optimization problem seeks to coordinate and synchronize the timing of traffic signals throughout a network in order to enhance traffic flow and reduce stops and delays.…
Sharp Restricted Isometry Bounds for the Inexistence of Spurious Local Minima in Nonconvex Matrix Recovery
Richard Y. Zhang, Somayeh Sojoudi, Javad Lavaei
Nonconvex matrix recovery is known to contain no spurious local minima under a restricted isometry property (RIP) with a sufficiently small RIP constant . If is too large, h…
How Much Restricted Isometry is Needed In Nonconvex Matrix Recovery?
Richard Y. Zhang, Cédric Josz, Somayeh Sojoudi +1
When the linear measurements of an instance of low-rank matrix recovery satisfy a restricted isometry property (RIP)---i.e. they are approximately norm-preserving---the problem is…
A theory on the absence of spurious solutions for nonconvex and nonsmooth optimization
Cedric Josz, Yi Ouyang, Richard Y. Zhang +2
We study the set of continuous functions that admit no spurious local optima (i.e. local minima that are not global minima) which we term \textit{global functions}. They satisfy va…
Large-Scale Sparse Inverse Covariance Estimation via Thresholding and Max-Det Matrix Completion
Richard Y. Zhang, Salar Fattahi, Somayeh Sojoudi
The sparse inverse covariance estimation problem is commonly solved using an -regularized Gaussian maximum likelihood estimator known as "graphical lasso", but its comput…
Sparse Inverse Covariance Estimation for Chordal Structures
Salar Fattahi, Richard Y. Zhang, Somayeh Sojoudi
In this paper, we consider the Graphical Lasso (GL), a popular optimization problem for learning the sparse representations of high-dimensional datasets, which is well-known to be…
Sparse Semidefinite Programs with Guaranteed Near-Linear Time Complexity via Dualized Clique Tree Conversion
Richard Y. Zhang, Javad Lavaei
Clique tree conversion solves large-scale semidefinite programs by splitting an matrix variable into up to smaller matrix variables, each representing a principal s…
Conic Optimization Theory: Convexification Techniques and Numerical Algorithms
Richard Y. Zhang, Cédric Josz, Somayeh Sojoudi
Optimization is at the core of control theory and appears in several areas of this field, such as optimal control, distributed control, system identification, robust control, state…
Modified Interior-Point Method for Large-and-Sparse Low-Rank Semidefinite Programs
Richard Y. Zhang, Javad Lavaei
Semidefinite programs (SDPs) are powerful theoretical tools that have been studied for over two decades, but their practical use remains limited due to computational difficulties i…
Parameter Insensitivity in ADMM-Preconditioned Solution of Saddle-Point Problems
Richard Y. Zhang, Jacob K. White
We consider the solution of linear saddle-point problems, using the alternating direction method-of-multipliers (ADMM) as a preconditioner for the generalized minimum residual meth…
GMRES-Accelerated ADMM for Quadratic Objectives
Richard Y. Zhang, Jacob K. White
We consider the sequence acceleration problem for the alternating direction method-of-multipliers (ADMM) applied to a class of equality-constrained problems with strongly convex qu…