Characterizations of the plenary hull of the generalized Jacobian matrix

DOI10.1007/BFb0120956zbMath0532.26007OpenAlexW61582801MaRDI QIDQ3314091

Jean-Baptiste Hiriart-Urruty

Publication date: 1982

Published in: Mathematical Programming Studies (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bfb0120956

zbMATH Keywords

set-valued functionsClarke's generalized gradientsgeneralized Jacobianslocally Lipschitz functionsplenary hull

Mathematics Subject Classification ID

Set-valued functions (26E25) Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Implicit function theorems, Jacobians, transformations with several variables (26B10) Special properties of functions of several variables, Hölder conditions, etc. (26B35)

Related Items

Support functions of the Clarke generalized Jacobian and of its plenary hull ⋮ Global univalence when mappings are not necessarily continuous ⋮ Generalized Hessian for \(C^{1,1}\) functions in infinite dimensional normed spaces ⋮ Multivalued exponentiation analysis. II: Recursive exponetials. ⋮ Second-order subdifferentials of \(C^{1,1}\) functions and optimality conditions ⋮ Separation via quadratic functions ⋮ Generalized second-order derivatives and optimality conditions ⋮ Second-order characterization of convex mappings in Banach spaces and its applications ⋮ Infinite dimensional generalized Jacobian: properties and calculus rules ⋮ Exponentiating a bundle of linear operators ⋮ Generalized derivatives for solutions of parametric ordinary differential equations with non-differentiable right-hand sides ⋮ The contingent and the paratingent as generalized derivatives for vector-valued and set-valued mappings ⋮ Stability in generalized differentiability based on a set convergence principle ⋮ Solving variational inequality problems via smoothing-nonsmooth reformulations ⋮ Generalized Hessian matrix and second-order optimality conditions for problems with \(C^{1,1}\) data ⋮ On generalized differentials and subdifferentials of Lipschitz vector-valued functions ⋮ Lipschitzian inverse functions, directional derivatives, and applications in \(C^{1,1}\) optimization

This page was built for publication: Characterizations of the plenary hull of the generalized Jacobian matrix