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Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a given set by a residual function, have proven to be extremely useful in analyzing the convergence rates of a host of iterative methods for solving optimization problems.
On Approximate Solutions of Systems of Linear Inequalities
A. J. Hoffman · 1952
Earlier work this paper cites.
Convex Analysis
R. T. Rockafellar · 1970
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An Implicit–Function Theorem for Generalized Variational Inequalities
S. M. Robinson · 1976
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Some Continuity Properties of Polyhedral Multifunctions
S. M. Robinson · 1981
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A Posteriori Error Bounds for the Linearly–Constrained Variational Inequality Problem
J.-S. Pang · 1987
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Matrix Perturbation Theory
G. W. Stewart and J. Sun · 1990
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Descent Methods for Convex Essentially Smooth Minimization
P. Tseng · 1991
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On the Linear Convergence of Descent Methods for Convex Essentially Smooth Minimization
Z.-Q. Luo and P. Tseng · 1992
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Characterization of the Subdifferential of Some Matrix Norms
G. A. Watson · 1992
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Error Bounds and Convergence Analysis of Feasible Descent Methods: A General Approach
Z.-Q. Luo and P. Tseng · 1993
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On the Convergence Rate of Dual Ascent Methods for Linearly Constrained Convex Minimization
Z.-Q. Luo and P. Tseng · 1993
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On Projection Algorithms for Solving Convex Feasibility Problems
H. H. Bauschke and J. M. Borwein · 1996
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Error Bounds in Mathematical Programming
J.-S. Pang · 1997
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Strong Conical Hull Intersection Property, Bounded Linear Regularity, Jameson’s Property (G), and Error Bounds in Convex Optimization
H. H. Bauschke, J. M. Borwein, and W. Li · 1999
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Error Bounds for Linear Matrix Inequalities
J. F. Sturm · 2000
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Optimal Hoffman–Type Estimates in Eigenvalue and Semidefinite Inequality Constraints
D. Azé and J.-B. Hiriart-Urruty · 2002
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Local Behavior of an Iterative Framework for Generalized Equations with Nonisolated Solutions
A. Fischer · 2002
Cited alongside, same era.
Strong Semismoothness of Eigenvalues of Symmetric Matrices and Its Application to Inverse Eigenvalue Problems
D. Sun and J. Sun · 2002
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Introductory Lectures on Convex Optimization: A Basic Course
Yu. Nesterov · 2004
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Signal Recovery by Proximal Forward–Backward Splitting
P. L. Combettes and V. R. Wajs · 2005
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Component Selection and Smoothing in Multivariate Nonparametric Regression
Y. Lin and H. H. Zhang · 2006
Error Bounds, Calmness and Their Applications in Nonsmooth Analysis
J.-P. Penot · 2010
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Approximation Accuracy, Gradient Methods, and Error Bound for Structured Convex Optimization
P. Tseng · 2010
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Recovering Low–Rank Matrices from Few Coefficients in Any Basis
D. Gross · 2011
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Fixed Point and Bregman Iterative Methods for Matrix Rank Minimization
S. Ma, D. Goldfarb, and L. Chen · 2011
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Optimization for Machine Learning
S. Sra, S. Nowozin, and S. J. Wright, editors · 2012
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On the Linear Convergence of the Proximal Gradient Method for Trace Norm Regularization
K. Hou, Z. Zhou, A. M.-C. So, and Z.-Q. Luo · 2013
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Calmness and Error Bounds for Convex Constraint Systems
W. Song · 2006
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Model Selection and Estimation in Regression with Grouped Variables
M. Yuan and Y. Lin · 2006
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Convex Multi–Task Feature Learning
A. Argyriou, T. Evgeniou, and M. Pontil · 2008
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Fixed–Point Continuation for ℓ 1 \ell_{1} –Minimization: Methodology and Convergence
E. T. Hale, W. Yin, and Y. Zhang · 2008
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The Group Lasso for Logistic Regression
L. Meier, S. van de Geer, and P. Bühlmann · 2008
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On Accelerated Proximal Gradient Methods for Convex–Concave Optimization
P. Tseng · 2008
Cited alongside, same era.
Beyond Convex Relaxation: A Polynomial–Time Non–Convex Optimization Approach to Network Localization
S. Ji, K.-F. Sze, Z. Zhou, A. M.-C. So, and Y. Ye · 2013
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Gradient Methods for Minimizing Composite Functions
Yu. Nesterov · 2013
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A Proximal–Gradient Homotopy Method for the Sparse Least–Squares Problem
L. Xiao and T. Zhang · 2013
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On the Linear Convergence of a Proximal Gradient Method for a Class of Nonsmooth Convex Minimization Problems
H. Zhang, J. Jiang, and Z.-Q. Luo · 2013
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An Introduction to a Class of Matrix Cone Programming
C. Ding, D. Sun, and K.-C. Toh · 2014
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Error Bounds and Metric Subregularity
A. Y. Kruger · 2015
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Error Bounds for Non–Polyhedral Convex Optimization and Applications to Linear Convergence of FDM and PGM
S. Pan and Y. Liu · 2015
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Coordinate Descent Algorithms
S. J. Wright · 2015
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Z. Zhou, Q. Zhang, and A. M.-C. So · 2015
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