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A. Ioffe, W. Churchill (2016)
METRIC REGULARITY—A SURVEY PART 1. THEORYJournal of the Australian Mathematical Society, 101
A. Jourani (2000)
Hoffman's Error Bound, Local Controllability, and Sensitivity AnalysisSIAM J. Control. Optim., 38
A. Kruger, H. Ngai, M. Théra (2010)
Stability of Error Bounds for Convex Constraint Systems in Banach SpacesSIAM J. Optim., 20
H. Gfrerer, J. Outrata (2016)
On Computation of Generalized Derivatives of the Normal-Cone Mapping and Their ApplicationsMath. Oper. Res., 41
A. Ioffe, J. Outrata (2008)
On Metric and Calmness Qualification Conditions in Subdifferential CalculusSet-Valued Analysis, 16
G Beer (1993)
Topologies on Closed and Closed Convex Sets, Mathematics and its Applications
J. Bolte, Trong Nguyen, J. Peypouquet, B. Suter (2015)
From error bounds to the complexity of first-order descent methods for convex functionsMathematical Programming, 165
A. Ioffe (2000)
Metric regularity and subdifferential calculusRussian Mathematical Surveys, 55
Xi Zheng, Zhou Wei (2012)
Perturbation Analysis of Error Bounds for Quasi-subsmooth Inequalities and Semi-infinite Constraint SystemsSIAM J. Optim., 22
R. Henrion, J. Outrata (2001)
A Subdifferential Condition for Calmness of MultifunctionsJournal of Mathematical Analysis and Applications, 258
A. Dontchev, R. Rockafellar (2009)
Implicit Functions and Solution Mappings: A View from Variational Analysis
L. Huang, K. Ng (2004)
On First- and Second-Order Conditions for Error BoundsSIAM J. Optim., 14
K. Ng, Xi Zheng (2001)
Error Bounds for Lower Semicontinuous Functions in Normed SpacesSIAM J. Optim., 12
E. Bednarczuk, A. Kruger (2011)
ERROR BOUNDS FOR VECTOR-VALUED FUNCTIONS ON METRIC SPACES
D. Noll, A. Rondepierre (2013)
On Local Convergence of the Method of Alternating ProjectionsFoundations of Computational Mathematics, 16
A. Lewis, J. Pang (1998)
Error Bounds for Convex Inequality Systems
A. Hoffman (1952)
On approximate solutions of systems of linear inequalitiesJournal of research of the National Bureau of Standards, 49
M. Cánovas, A. Kruger, M. López, J. Parra, M. Théra (2013)
Calmness Modulus of Linear Semi-infinite ProgramsSIAM J. Optim., 24
A. Kruger (2014)
Error bounds and metric subregularityOptimization, 64
D. Azé, J. Corvellec (2004)
Characterizations of error bounds for lower semicontinuous functions on metric spacesESAIM: Control, Optimisation and Calculus of Variations, 10
O. Cornejo, A. Jourani, C. Zălinescu (1997)
Conditioning and Upper-Lipschitz Inverse Subdifferentials in Nonsmooth Optimization ProblemsJournal of Optimization Theory and Applications, 95
(1997)
Error bounds inmathematical programming.Math
S. Robinson (1975)
An Application of Error Bounds for Convex Programming in a Linear SpaceSiam Journal on Control, 13
Minghua Li, K. Meng, Xiaoqi Yang (2016)
On error bound moduli for locally Lipschitz and regular functionsMathematical Programming, 171
M. Fabian, R. Henrion, A. Kruger, J. Outrata (2010)
Error Bounds: Necessary and Sufficient ConditionsSet-Valued and Variational Analysis, 18
A. Kruger (2014)
Error Bounds and Hölder Metric SubregularitySet-Valued and Variational Analysis, 23
H. Ngai, A. Kruger, M. Théra (2010)
Stability of Error Bounds for Semi-infinite Convex Constraint SystemsSIAM J. Optim., 20
R. Hesse, D. Luke (2012)
Nonconvex Notions of Regularity and Convergence of Fundamental Algorithms for Feasibility ProblemsSIAM J. Optim., 23
Guoyin Li, B. Mordukhovich (2012)
Hölder Metric Subregularity with Applications to Proximal Point MethodSIAM J. Optim., 22
M. Fabian, R. Henrion, A. Kruger, J. Outrata (2011)
About error bounds in metric spaces
K. Meng, X. Yang (2012)
Equivalent Conditions for Local Error BoundsSet-Valued and Variational Analysis, 20
H. Ngai, M. Théra (2004)
Error Bounds and Implicit Multifunction Theorem in Smooth Banach Spaces and Applications to OptimizationSet-Valued Analysis, 12
P. Combettes (1996)
The Convex Feasibility Problem in Image RecoveryAdvances in Imaging and Electron Physics, 95
JM Borwein, JD Vanderwerff (2010)
Convex Functions: constructions, Characterizations and Counterexamples, Encyclopedia of Mathematics and its Applications
I. Ekeland (1974)
On the variational principleJournal of Mathematical Analysis and Applications, 47
A. Kruger (2015)
Nonlinear Metric SubregularityJournal of Optimization Theory and Applications, 171
A. Beck, M. Teboulle (2003)
Convergence rate analysis and error bounds for projection algorithms in convex feasibility problemsOptimization Methods and Software, 18
(1951)
Quelques classes de problémes extrémaux
H. Ngai, M. Théra (2008)
Error Bounds in Metric Spaces and Application to the Perturbation Stability of Metric RegularitySIAM J. Optim., 19
RT Rockafellar, RJB Wets (1998)
Variational Analysis
A. Lewis, D. Luke, J. Malick (2015)
Local linear convergence of alternating and averaged nonconvex projections
D. Azé (2003)
A survey on error bounds for lower semicontinuous functionsEsaim: Proceedings, 13
Heinz Bauschke, J. Borwein (1996)
On Projection Algorithms for Solving Convex Feasibility ProblemsSIAM Rev., 38
C. Zălinescu (2003)
Sharp Estimates for Hoffman's Constant for Systems of Linear Inequalities and EqualitiesSIAM J. Optim., 14
H. Gfrerer (2011)
First Order and Second Order Characterizations of Metric Subregularity and Calmness of Constraint Set MappingsSIAM J. Optim., 21
H. Ngai, Huu Nguyen, M. Théra (2013)
Metric Regularity of the Sum of Multifunctions and ApplicationsJournal of Optimization Theory and Applications, 160
D. Azé (2006)
A Unified Theory for Metric Regularity of Multifunctions
H. Ngai, Huu Nguyen, M. Théra (2013)
Implicit multifunction theorems in complete metric spacesMathematical Programming, 139
E. Bednarczuk, A. Kruger (2012)
Error bounds for vector-valued functions: Necessary and sufficient conditionsNonlinear Analysis-theory Methods & Applications, 75
(2010)
Error bounds, calmness and their applications in nonsmooth analysis
H. Ngai, M. Théra (2008)
Error bounds for systems of lower semicontinuous functions in Asplund spacesMathematical Programming, 116
PL Combettes (1996)
Advances in Imaging and Electron Physics
M. Cánovas, A. Hantoute, J. Parra, F. Toledo-Moreo (2015)
Boundary of subdifferentials and calmness moduli in linear semi-infinite optimizationOptimization Letters, 9
Alexander Kruger, D. Luke, H. Nguyen, Thao (2016)
Set regularities and feasibility problemsMathematical Programming, 168
D. Drusvyatskiy, A. Ioffe, A. Lewis (2012)
Curves of DescentSIAM J. Control. Optim., 53
M. Cánovas, R. Henrion, M. López, J. Parra (2015)
Outer Limit of Subdifferentials and Calmness Moduli in Linear and Nonlinear ProgrammingJournal of Optimization Theory and Applications, 169
A. Kruger, N. Thao (2015)
Regularity of collections of sets and convergence of inexact alternating projectionsarXiv: Optimization and Control
A. Auslender, J. Crouzeix (1988)
Global Regularity TheoremsMath. Oper. Res., 13
Zili Wu, J. Ye (2002)
Sufficient Conditions for Error BoundsSIAM J. Optim., 12
A. Ioffe (2016)
METRIC REGULARITY—A SURVEY PART II. APPLICATIONSJournal of the Australian Mathematical Society, 101
J. Borwein, J. Vanderwerff (2010)
Convex Functions: Constructions, Characterizations and Counterexamples
F. Giannessi (2006)
Variational Analysis and Generalized DifferentiationJournal of Optimization Theory and Applications, 131
Xi Zheng, K. Ng (2012)
Metric subregularity for proximal generalized equations in Hilbert spacesNonlinear Analysis-theory Methods & Applications, 75
O. Mangasarian (1985)
A Condition Number for Differentiable Convex InequalitiesMath. Oper. Res., 10
H. Ngai, M. Théra (2005)
Error bounds for convex differentiable inequality systems in Banach spacesMathematical Programming, 104
D. Klatte, Wu Li (1999)
Asymptotic constraint qualifications and global error bounds for convex inequalitiesMathematical Programming, 84
Xi Zheng, K. Ng (2010)
Metric Subregularity and Calmness for Nonconvex Generalized Equations in Banach SpacesSIAM J. Optim., 20
Y. Censor (1984)
Iterative Methods for the Convex Feasibility ProblemNorth-holland Mathematics Studies, 87
J. Borwein, Guoyin Li, Liangjin Yao (2013)
Analysis of the Convergence Rate for the Cyclic Projection Algorithm Applied to Basic Semialgebraic Convex SetsSIAM J. Optim., 24
J. Corvellec, V. Motreanu (2008)
Nonlinear error bounds for lower semicontinuous functions on metric spacesMathematical Programming, 114
G. Beer (1993)
Topologies on Closed and Closed Convex Sets
J. Burke, S. Deng (2005)
Weak sharp minima revisited, part II: application to linear regularity and error boundsMathematical Programming, 104
R. Henrion, A. Jourani (2002)
Subdifferential Conditions for Calmness of Convex ConstraintsSIAM J. Optim., 13
Our aim in the current article is to extend the developments in Kruger et al. (SIAM J Optim 20(6):3280–3296, 2010. doi: 10.1137/100782206 ) and, more precisely, to characterize, in the Banach space setting, the stability of the local and global error bound property of inequalities determined by lower semicontinuous functions under data perturbations. We propose new concepts of (arbitrary, convex and linear) perturbations of the given function defining the system under consideration, which turn out to be a useful tool in our analysis. The characterizations of error bounds for families of perturbations can be interpreted as estimates of the ‘radius of error bounds’. The definitions and characterizations are illustrated by examples.
Mathematical Programming – Springer Journals
Published: Mar 9, 2017
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