Calculus rules on a new set—valued second order derivative for convex functions

DOI10.1016/0362-546X(89)90090-4zbMath0705.26013OpenAlexW1984222574MaRDI QIDQ3485109

Alberto Seeger, Jean-Baptiste Hiriart-Urruty

Publication date: 1989

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(89)90090-4

zbMATH Keywords

convex functioncomposite functionsnonsmooth functionsecond order directional derivativesecond order set-value derivatives

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Continuity and differentiation questions (26B05) Convexity of real functions of several variables, generalizations (26B25)

Related Items (19)

Second-order subgradients of convex integral functionals ⋮ Graphical methods in first and second-order differentiability theory of integral functionals ⋮ Calculus rules for combinations of ellipsoids and applications ⋮ Piecewise Ck functions in nonsmooth analysis ⋮ Second order epi derivatives and the Dupin indicatrix for nonsmooth functions ⋮ Second-order normal vectors to a convex epigraph ⋮ First and second order sufficient conditions for strict minimality in nonsmooth vector optimization. ⋮ Conjugation and second-order properties of convex functions ⋮ Complément de Schur et sous-différentiel du second ordre d'une fonction convexe ⋮ Second-order necessary and sufficient optimality conditions for constrained vector equilibrium problem with applications ⋮ Direct and inverse addition in convex analysis: The continuous case ⋮ Second Order Differentiability of Convex Functions in Banach Spaces ⋮ Approximations, expansions and univalued representations of multifunctions ⋮ Sensitivity Analysis of Variational Inequalities via Twice Epi-differentiability and Proto-differentiability of the Proximity Operator ⋮ Conciliating Generalized Derivatives ⋮ Generalized Second Derivatives of Convex Functions and Saddle Functions ⋮ First- and second-order epi-differentiability in eigenvalue optimization ⋮ On relations and applications of generalized second-order directional derivatives ⋮ Limiting behavior of the approximate second-order subdifferential of a convex function

Cites Work

• Calculus Rules on the Approximate Second-Order Directional Derivative of a Convex Function
• Second Order Directional Derivatives in Parametric Optimization Problems
• Lipschitz $r$-continuity of the approximative subdifferential of a convex function.
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