An open mapping theorem using unbounded generalized Jacobians

DOI10.1016/S0362-546X(01)00774-XzbMath1035.49016OpenAlexW2076959604MaRDI QIDQ1612598

Vaithilingam Jeyakumar, Dinh The Luc

Publication date: 25 August 2002

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0362-546x(01)00774-x

zbMATH Keywords

implicit function theoremopen mapping theoreminverse function theoremapproximate Jacobian

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Implicit function theorems, Jacobians, transformations with several variables (26B10) Open mapping and closed graph theorems; completeness (including (B)-, (B_r)-completeness) (46A30)

Related Items (8)

Equi-surjective systems of linear operators and applications ⋮ Regularity properties of constrained set-valued mappings ⋮ Normal coderivative for multifunctions and implicit function theorems ⋮ Convexifactors, generalized convexity and vector optimization ⋮ Chain rules for approximate Jacobians of continuous functions ⋮ Inversion of nonsmooth maps between Banach spaces ⋮ Solution point characterizations and convergence analysis of a descent algorithm for nonsmooth continuous complementarity problems. ⋮ Global inversion of nonsmooth mappings using pseudo-Jacobian matrices

Cites Work

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• Fat homeomorphisms and unbounded derivate containers
• On the inverse function theorem
• Nonsmooth calculus, minimality, and monotonicity of convexificators
• Lipschitzian inverse functions, directional derivatives, and applications in \(C^{1,1}\) optimization
• Generalized differential calculus for nonsmooth and set-valued mappings
• Convergence of asymptotic directions
• Extensions of subgradient calculus with applications to optimization
• Recession maps and applications
• An Implicit Function Theorem without Differentiability
• Approximate Jacobian Matrices for Nonsmooth Continuous Maps and C¹-Optimization
• Mixed Coderivatives of Set–Valued Mappings in Variational Analysis
• Approximate Hessian matrices and second-order optimality conditions for nonlinear programming problems with C¹-data
• A survey of subdifferential calculus with applications

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