Nonconvex Robust Low-Rank Matrix Recovery

DOI10.1137/18M1224738MaRDI QIDQ5217366

Zhihui Zhu, Anthony Man-Cho So, Xiao Li, René Victor Valqui Vidal

Publication date: 27 February 2020

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.09237

zbMATH Keywords

subgradient methodsharpnessrobust PCAweak convexityrobust low-rank matrix recovery

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Analysis of algorithms (68W40) Nonconvex programming, global optimization (90C26) Numerical optimization and variational techniques (65K10) Statistical aspects of information-theoretic topics (62B10)

Related Items

Unnamed Item ⋮ Nonsmooth rank-one matrix factorization landscape ⋮ A low-rank spectral method for learning Markov models ⋮ Adaptive iterative hard thresholding for low-rank matrix recovery and rank-one measurements ⋮ Exact Recovery of Multichannel Sparse Blind Deconvolution via Gradient Descent ⋮ The global optimization geometry of shallow linear neural networks ⋮ Low-rank matrix recovery with composite optimization: good conditioning and rapid convergence ⋮ Weakly Convex Optimization over Stiefel Manifold Using Riemannian Subgradient-Type Methods ⋮ Non-convex exact community recovery in stochastic block model ⋮ Unnamed Item ⋮ Low rank matrix recovery with adversarial sparse noise*

Uses Software

• SDPLR

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A perturbation inequality for concave functions of singular values and its applications in low-rank matrix recovery
• A framework for robust subspace learning
• A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization
• Subgradient methods for sharp weakly convex functions
• Local minima and convergence in low-rank semidefinite programming
• Exact matrix completion via convex optimization
• Fast and Near-Optimal Matrix Completion via Randomized Basis Pursuit
• Guaranteed Matrix Completion via Non-Convex Factorization
• Exact and Stable Covariance Estimation From Quadratic Sampling via Convex Programming
• Robust principal component analysis?
• Strong and Weak Convexity of Sets and Functions
• Weak Sharp Minima in Mathematical Programming
• The learnability of quantum states
• On convergence rates of subgradient optimization methods
• Variational Analysis
• Low-Rank Positive Semidefinite Matrix Recovery From Corrupted Rank-One Measurements
• Global Optimality in Low-Rank Matrix Optimization
• On the Quadratic Convergence of the Cubic Regularization Method under a Local Error Bound Condition
• Solving (most) of a set of quadratic equalities: composite optimization for robust phase retrieval
• Non-convex low-rank matrix recovery with arbitrary outliers via median-truncated gradient descent
• Symmetry, Saddle Points, and Global Optimization Landscape of Nonconvex Matrix Factorization
• Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview
• The non-convex geometry of low-rank matrix optimization
• Tight Oracle Inequalities for Low-Rank Matrix Recovery From a Minimal Number of Noisy Random Measurements
• Recovering Low-Rank Matrices From Few Coefficients in Any Basis
• Restricted $p$-Isometry Properties of Nonconvex Matrix Recovery
• Minimization of unsmooth functionals
• The nonsmooth landscape of phase retrieval

This page was built for publication: Nonconvex Robust Low-Rank Matrix Recovery