Mean-value theorem with small subdifferentials

DOI10.1023/A:1022672005994zbMath0891.49009OpenAlexW30268464MaRDI QIDQ1367795

Jean-Paul Penot

Publication date: 9 July 1998

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1022672005994

zbMATH Keywords

nonsmooth analysisgeneralized derivativessubdifferentialsfuzzy calculusmean-value theorem

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Derivatives of functions in infinite-dimensional spaces (46G05)

Related Items (10)

Lipschitzian properties of integral functionals on Lebesgue spaces \(L_p, 1 \leqslant p < \infty\) ⋮ Approximately convex functions and approximately monotonic operators ⋮ Generalized monotonicity of subdifferentials and generalized convexity ⋮ A mean value theorem for tangentially convex functions ⋮ Directionally limiting subdifferentials and second-order optimality conditions ⋮ Nonsmooth sequential analysis in Asplund spaces ⋮ Ekeland Duality as a Paradigm ⋮ Softness, sleekness and regularity properties in nonsmooth analysis ⋮ Subdifferential calculus for a quasiconvex function with generator ⋮ Multidirectional Mean Value Inequalities in Quasidifferential Calculus

Cites Work

• Mean value theorems and sufficient optimality conditions for nonsmooth functions
• Properties of generalized differentials
• The differentiability of real functions on normed linear space using generalized subgradients
• Convex functions, monotone operators and differentiability
• Mean value theorem for convex functions
• Generalized monotonicity of subdifferentials and generalized convexity
• A mean value theorem for semidifferentiable functions
• Integration of subdifferentials of lower semicontinuous functions on Banach spaces
• Approximate mean value theorem for upper subderivatives
• A note on the equivalence between the mean value theorem for the dim derivative and the Clarke-Rockafellar derivative
• Optimization and nonsmooth analysis
• Subdifferentials, Local ε-Supports and Asplund Spaces
• On the mean value theorem
• Subgradient Criteria for Monotonicity, The Lipschitz Condition, and Convexity
• Sub differential Monotonicity as Characterization of Convex Functions
• Mean Value Property and Subdifferential Criteria for Lower Semicontinuous Functions
• Nonsmooth sequential analysis in Asplund spaces
• Proximal Analysis and Approximate Subdifferentials
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