On the mean value theorem

DOI10.1080/02331938808843330zbMath0661.49008OpenAlexW2018488325MaRDI QIDQ3810432

Jean-Paul Penot

Publication date: 1988

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331938808843330

zbMATH Keywords

mean value theoremnonsmooth functionsDini-Hadamard derivatives

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Continuity and differentiation questions (26B05)

Related Items (15)

Generalized monotonicity and generalized convexity ⋮ Mean-value theorem with small subdifferentials ⋮ A note on the equivalence between the mean value theorem for the dim derivative and the Clarke-Rockafellar derivative ⋮ A generalized mean-value theorem and optimality conditions in composite nonsmooth minimization ⋮ Fixed point theorem in nonsmooth analysis and its applications ⋮ Necessary and sufficient optimality conditions for fractional multi-objective problems ⋮ A strong mean value theorem and applications ⋮ Necessary optimality conditions for bilevel set optimization problems ⋮ Local minimality versus spongious minimality ⋮ Conciliating Generalized Derivatives ⋮ Necessary optimality conditions for bilevel optimization problems using convexificators ⋮ Mean Value Property and Subdifferential Criteria for Lower Semicontinuous Functions ⋮ Multidirectional Mean Value Inequalities in Quasidifferential Calculus ⋮ Mean value properties of nondifferentiation functions and their application in nonsmooth analysis ⋮ Nonsmooth calculus, minimality, and monotonicity of convexificators

Cites Work

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• Calcul sous-différentiel et optimisation
• Generalized Gradients, Lipschitz behavior and Directional Derivatives
• Optimization and nonsmooth analysis
• The drop theorem, the petal theorem and Ekeland's variational principle
• Nonconvex minimization problems
• Mean value theorems in nonsmooth analysis

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