On regularity concepts in variational analysis

DOI10.1007/s11784-010-0021-0zbMath1205.49023OpenAlexW2046370168MaRDI QIDQ626539

Alexander D. Ioffe

Publication date: 18 February 2011

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

Full work available at URL: https://doi.org/10.1007/s11784-010-0021-0

zbMATH Keywords

stabilityset-valued mappingstrong regularitycalmnessmetric regularitysurjection (covering)

Mathematics Subject Classification ID

Sensitivity, stability, parametric optimization (90C31) Set-valued and variational analysis (49J53) Set-valued functions (26E25) Perturbation theory of linear operators (47A55) Open mapping and closed graph theorems; completeness (including (B)-, (B_r)-completeness) (46A30)

Related Items (15)

Towards variational analysis in metric spaces: metric regularity and fixed points ⋮ An Induction Theorem and Nonlinear Regularity Models ⋮ Directional Metric Regularity of Multifunctions ⋮ Implicit multifunction theorems in complete metric spaces ⋮ Directional metric pseudo subregularity of set-valued mappings: a general model ⋮ Projectional coderivatives and calculus rules ⋮ Nonlinear metric regularity on fixed sets ⋮ Higher-Order Karush--Kuhn--Tucker Conditions in Nonsmooth Optimization ⋮ Unnamed Item ⋮ On covering properties in variational analysis and optimization ⋮ Directional Hölder metric regularity ⋮ REGULARITY PROPERTIES IN VARIATIONAL ANALYSIS AND APPLICATIONS IN OPTIMISATION ⋮ Error bounds and metric subregularity ⋮ Regularity of Newton's iteration for general parametric variational system ⋮ Metric regularity relative to a cone

Cites Work

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• Equivalent formulations of Ekeland's variational principle
• Restrictive metric regularity and generalized differential calculus in Banach spaces
• Regularity and conditioning of solution mappings in variational analysis
• Directional metric regularity of mappings and stability theorems
• Techniques of variational analysis
• Strongly Regular Generalized Equations
• LYUSTERNIK'S THEOREM AND THE THEORY OF EXTREMA
• Generalized equations and their solutions, Part I: Basic theory
• Metric regularity and subdifferential calculus
• Variational Analysis and Generalized Differentiation I
• Directional Stability Theorem and Directional Metric Regularity

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