Quantitative characterizations of regularity properties of collections of sets

DOI10.1007/s10957-014-0556-0zbMath1309.49016arXiv1309.7002OpenAlexW3104613222MaRDI QIDQ2260647

Alexander Y. Kruger, Nguyen Hieu Thao

Publication date: 11 March 2015

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.7002

zbMATH Keywords

set-valued mappingsnormal conesubdifferentialmetric regularitycollections of sets

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Set-valued and variational analysis (49J53) Optimality conditions for problems in abstract spaces (49K27)

Related Items

Primal necessary characterizations of transversality properties ⋮ Dual sufficient characterizations of transversality properties ⋮ On semiregularity of mappings ⋮ About extensions of the extremal principle ⋮ On ranges of set-valued mappings ⋮ Some new characterizations of intrinsic transversality in Hilbert spaces ⋮ Set regularities and feasibility problems ⋮ Geometric and metric characterizations of transversality properties ⋮ Transversality and alternating projections for nonconvex sets ⋮ The radius of metric subregularity ⋮ About \([q\)-regularity properties of collections of sets] ⋮ Special Issue dedicated to the 65th birthday of Alexander Kruger ⋮ About intrinsic transversality of pairs of sets ⋮ About subtransversality of collections of sets ⋮ A convergent relaxation of the Douglas-Rachford algorithm ⋮ Convex combination of alternating projection and Douglas-Rachford operators for phase retrieval ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Transversality properties: primal sufficient conditions ⋮ Metric inequality conditions on sets and consequences in optimization ⋮ Necessary conditions for linear convergence of iterated expansive, set-valued mappings ⋮ REGULARITY PROPERTIES IN VARIATIONAL ANALYSIS AND APPLICATIONS IN OPTIMISATION ⋮ Quantitative Convergence Analysis of Iterated Expansive, Set-Valued Mappings ⋮ Extremality, stationarity and generalized separation of collections of sets ⋮ On tangential transversality ⋮ Phase Retrieval with Sparse Phase Constraint

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• About \([q\)-regularity properties of collections of sets]
• Enhanced metric regularity and Lipschitzian properties of variational systems
• Local linear convergence of approximate projections onto regularized sets
• Metric subregularity for proximal generalized equations in Hilbert spaces
• Convexity and well-posed problems
• Local linear convergence for alternating and averaged nonconvex projections
• Uniform subsmoothness and linear regularity for a collection of infinitely many closed sets
• About stationarity and regularity in variational analysis
• On the convergence of von Neumann's alternating projection algorithm for two sets
• On Fréchet subdifferentials
• Asymptotic constraint qualifications and global error bounds for convex inequalities.
• Strong conical hull intersection property, bounded linear regularity, Jameson's property \((G)\), and error bounds in convex optimization
• On the variational principle
• Regularity and conditioning of solution mappings in variational analysis
• Stationarity and regularity of infinite collections of sets: applications to infinitely constrained optimization
• Stationarity and regularity of infinite collections of sets
• On subregularity properties of set-valued mappings
• Prox-regularity of rank constraint sets and implications for algorithms
• About regularity of collections of sets
• Weak sharp minima revisited. II: Application to linear regularity and error bounds
• Constraint Qualifications for Semi-Infinite Systems of Convex Inequalities
• Calculus Without Derivatives
• Metric Subregularity and Calmness for Nonconvex Generalized Equations in Banach Spaces
• Strict (ε, δ)-Subdifferentials and Extremality Conditions
• Subsmooth sets: Functional characterizations and related concepts
• Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality
• Approximate subdifferentials and applications 3: the metric theory
• Metric Subregularity and Constraint Qualifications for Convex Generalized Equations in Banach Spaces
• The SECQ, Linear Regularity, and the Strong CHIP for an Infinite System of Closed Convex Sets in Normed Linear Spaces
• Implicit Functions and Solution Mappings
• Linear Regularity for a Collection of Subsmooth Sets in Banach Spaces
• Metric regularity, openness and Lipschitzian behavior of multifunctions
• Variational Analysis
• Metric regularity and subdifferential calculus
• On Projection Algorithms for Solving Convex Feasibility Problems
• The radius of metric regularity
• Weak Stationarity: Eliminating the gap between necessary and sufficient conditions
• About uniform regularity of collections of sets
• Nonconvex Notions of Regularity and Convergence of Fundamental Algorithms for Feasibility Problems
• Strong CHIP, normality, and linear regularity of convex sets
• Metric inequality, subdifferential calculus and applications