Equivalent conditions for local error bounds

DOI10.1007/s11228-012-0217-0zbMath1254.49011OpenAlexW1967024019MaRDI QIDQ1928763

Xiao Qi Yang, Kaiwen Meng

Publication date: 4 January 2013

Published in: Set-Valued and Variational Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11228-012-0217-0

zbMATH Keywords

error boundssubdifferentialnormal conessubderivativestrong slope

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Set-valued and variational analysis (49J53) Set-valued and function-space-valued mappings on manifolds (58C06)

Related Items

Error bounds revisited, Perturbation of error bounds, An approach to calmness of linear inequality systems from Farkas lemma, Constraint qualifications in terms of convexificators for nonsmooth programming problems with mixed constraints, Calmness of partial perturbation to composite rank constraint systems and its applications, METRIC REGULARITY—A SURVEY PART 1. THEORY, Error Bounds and Multipliers in Constrained Optimization Problems with Tolerance, Calmness of partially perturbed linear systems with an application to the central path, Point-based neighborhoods for sharp calmness constants in linear programming, On error bound moduli for locally Lipschitz and regular functions, Hölder error bounds and Hölder calmness with applications to convex semi-infinite optimization, Error bounds and metric subregularity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On error bounds for quasinormal programs
• On metric and calmness qualification conditions in subdifferential calculus
• Error bounds: necessary and sufficient conditions
• New uniform parametric error bounds
• Generalized differential calculus for nonsmooth and set-valued mappings
• Error bounds in mathematical programming
• Global error bounds with fractional exponents
• Variational pairs and applications to stability in nonsmooth analysis.
• On error bounds for lower semicontinuous functions.
• Regularity and conditioning of solution mappings in variational analysis
• The Fritz John necessary optimality conditions in the presence of equality and inequality constraints
• Calmness of constraint systems with applications
• On weak sharp minima for a special class of nonsmooth functions
• Error Bounds for Lower Semicontinuous Functions in Normed Spaces
• Sufficient Conditions for Error Bounds
• Weak Sharp Minima in Mathematical Programming
• Error Bounds in Metric Spaces and Application to the Perturbation Stability of Metric Regularity
• Regular Points of Lipschitz Functions
• Nonconvex minimization problems
• A survey on error bounds for lower semicontinuous functions
• First-Order and Second-Order Conditions for Error Bounds
• On First- and Second-Order Conditions for Error Bounds
• Weak Sharp Minima: Characterizations and Sufficient Conditions
• Hoffman's Error Bound, Local Controllability, and Sensitivity Analysis
• Characterizations of error bounds for lower semicontinuous functions on metric spaces