128 citations · 540 across the 44 of their papers we have counts for
11 papers · 1 filter
Second-Order KKT Guarantees for Bregman ADMM in Nonconvex and Non-Lipschitz Optimization
Shuang Li, Zhihui Zhu, Qiuwei Li
We analyze Bregman ADMM for nonconvex linearly constrained problems under two-sided relative smoothness, a condition that replaces the standard Lipschitz gradient assumption with a…
A Validation Approach to Over-parameterized Matrix and Image Recovery
Lijun Ding, Zhen Qin, Liwei Jiang +2
This paper studies the problem of recovering a low-rank matrix from several noisy random linear measurements. We consider the setting where the rank of the ground-truth matrix is u…
Rank Overspecified Robust Matrix Recovery: Subgradient Method and Exact Recovery
Lijun Ding, Liwei Jiang, Yudong Chen +2
We study the robust recovery of a low-rank matrix from sparsely and grossly corrupted Gaussian measurements, with no prior knowledge on the intrinsic rank. We consider the robust m…
Half-Space Proximal Stochastic Gradient Method for Group-Sparsity Regularized Problem
Tianyi Chen, Guanyi Wang, Tianyu Ding +3
Optimizing with group sparsity is significant in enhancing model interpretability in machining learning applications, e.g., feature selection, compressed sensing and model compress…
Orthant Based Proximal Stochastic Gradient Method for -Regularized Optimization
Tianyi Chen, Tianyu Ding, Bo Ji +6
Sparsity-inducing regularization problems are ubiquitous in machine learning applications, ranging from feature selection to model compression. In this paper, we present a novel st…
The Global Geometry of Centralized and Distributed Low-rank Matrix Recovery without Regularization
Shuang Li, Qiuwei Li, Zhihui Zhu +2
Low-rank matrix recovery is a fundamental problem in signal processing and machine learning. A recent very popular approach to recovering a low-rank matrix X is to factorize it as…
Weakly Convex Optimization over Stiefel Manifold Using Riemannian Subgradient-Type Methods
Xiao Li, Shixiang Chen, Zengde Deng +3
We consider a class of nonsmooth optimization problems over the Stiefel manifold, in which the objective function is weakly convex in the ambient Euclidean space. Such problems are…
Incremental Methods for Weakly Convex Optimization
Xiao Li, Zhihui Zhu, Anthony Man-Cho So +1
Incremental methods are widely utilized for solving finite-sum optimization problems in machine learning and signal processing. In this paper, we study a family of incremental meth…
Provable Bregman-divergence based Methods for Nonconvex and Non-Lipschitz Problems
Qiuwei Li, Zhihui Zhu, Gongguo Tang +1
The (global) Lipschitz smoothness condition is crucial in establishing the convergence theory for most optimization methods. Unfortunately, most machine learning and signal process…
Global Optimality in Distributed Low-rank Matrix Factorization
Zhihui Zhu, Qiuwei Li, Xinshuo Yang +2
We study the convergence of a variant of distributed gradient descent (DGD) on a distributed low-rank matrix approximation problem wherein some optimization variables are used for…
Convergence Analysis of Alternating Projection Method for Nonconvex Sets
Zhihui Zhu, Xiao Li
Alternating projection method has been used in a wide range of engineering applications since it is a gradient-free method (without requiring tuning the step size) and usually has…