Metric regularity of mappings and generalized normals to set images

DOI10.1007/s11228-009-0122-3zbMath1218.49023OpenAlexW2125630089MaRDI QIDQ1044250

Nguyen Mau Nam, Boris S. Mordukhovich, Bingwu Wang

Publication date: 11 December 2009

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

Full work available at URL: https://digitalcommons.wayne.edu/cgi/viewcontent.cgi?article=1060&context=math_reports

zbMATH Keywords

normal conesvariational analysismetric regularitycoderivativesgeneralized differentiationcalculus rulesset images

Mathematics Subject Classification ID

Sensitivity, stability, parametric optimization (90C31) Nonsmooth analysis (49J52) Set-valued and variational analysis (49J53) Geometry and structure of normed linear spaces (46B20) Differentiation theory (Gateaux, Fréchet, etc.) on manifolds (58C20)

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Cites Work

• Unnamed Item
• Unnamed Item
• Nonsmooth analysis
• Nonsmooth equations in optimization. Regularity, calculus, methods and applications
• Calculus of sequential normal compactness in variational analysis.
• Sequential normal compactness versus topological normal compactness in variational analysis.
• Techniques of variational analysis
• Variational analysis and mathematical economics 1: Subdifferential calculus and the second theorem of welfare economics
• Directional Regularity and Metric Regularity
• Optimization and nonsmooth analysis
• A Smooth Variational Principle With Applications to Subdifferentiability and to Differentiability of Convex Functions
• Regular Points of Lipschitz Functions
• LYUSTERNIK'S THEOREM AND THE THEORY OF EXTREMA
• Coderivatives of multivalued mappings, locally compact cones and metric regularity
• Complete Characterization of Openness, Metric Regularity, and Lipschitzian Properties of Multifunctions
• Metric regularity and subdifferential calculus
• Tangential approximations
• The radius of metric regularity