Fréchet and normal coderivatives of implicit multifunctions

DOI10.1080/00036811.2010.483432zbMath1225.49022OpenAlexW2011283660WikidataQ58303310 ScholiaQ58303310MaRDI QIDQ3006692

Nguyen Dong Yen, Gue Myung Lee

Publication date: 20 June 2011

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036811.2010.483432

zbMATH Keywords

upper estimateimplicit multifunctionlower estimateFréchet coderivativenormal coderivative

Mathematics Subject Classification ID

Set-valued and variational analysis (49J53) Fréchet and Gateaux differentiability in optimization (49J50) Implicit function theorems, Jacobians, transformations with several variables (26B10)

Related Items

Coderivatives of implicit multifunctions and stability of variational systems ⋮ Coderivatives of a Karush-Kuhn-Tucker point set map and applications ⋮ Stability of generalized equations under nonlinear perturbations ⋮ Variational inequalities over Euclidean balls ⋮ Nonlinear perturbations of polyhedral normal cone mappings and affine variational inequalities ⋮ Linearly perturbed polyhedral normal cone mappings and applications ⋮ A note on implicit multifunction theorems ⋮ Sensitivity analysis of a stationary point set map under total perturbations. I: Lipschitzian stability ⋮ Sensitivity analysis of a stationary point set map under total perturbations. II: Robinson stability ⋮ Stability for trust-region methods via generalized differentiation ⋮ Lipschitzian stability of parametric variational inequalities over perturbed polyhedral convex sets

Cites Work

• Relationships between Robinson metric regularity and Lipschitz-like behavior of implicit multifunctions
• Point-based sufficient conditions for metric regularity of implicit multifunctions
• Generalized differential calculus for nonsmooth and set-valued mappings
• Coderivatives in parametric optimization
• Implicit multifunction theorems
• Normal coderivative for multifunctions and implicit function theorems
• Coderivative analysis of variational systems
• Variational Analysis
• Solution Stability of Nonsmooth Continuous Systems with Applications to Cone-Constrained Optimization