Subdifferential estimate of the directional derivative, optimality criterion and separation principles

DOI10.1080/02331934.2011.645034zbMath1278.49019OpenAlexW2082572991MaRDI QIDQ5891369

Marc Lassonde, Florence Jules

Publication date: 19 December 2013

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331934.2011.645034

zbMATH Keywords

lower semicontinuitysubdifferentialseparation principlemean value inequalitydirectional derivativeoptimality criteriamaximal monotonicity\(\varepsilon\)-subdifferential

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Convexity of real functions of several variables, generalizations (26B25) Inequalities involving derivatives and differential and integral operators (26D10) Optimality conditions for problems in abstract spaces (49K27)

Related Items (8)

Links between functions and subdifferentials ⋮ Links between subderivatives and subdifferentials ⋮ Unnamed Item ⋮ Characterization of the monotone polar of subdifferentials ⋮ Upper semismooth functions and the subdifferential determination property ⋮ Subdifferential test for optimality ⋮ Valadier-like formulas for the supremum function I ⋮ Differential stability of convex optimization problems under weaker conditions

Cites Work

• A note on epsilon-subgradients and maximal monotonicity
• Links between directional derivatives through multidirectional mean value inequalities
• The equivalence of several basic theorems for subdifferentials
• Fuzzy principles and characterization of trustworthiness
• Subdifferential calculus using \(\varepsilon\)-subdifferentials
• The least slope of a convex function and the maximal monotonicity of its subdifferential
• Integration of subdifferentials of lower semicontinuous functions on Banach spaces
• On the variational principle
• Characterization of the subdifferentials of convex functions
• On the maximal monotonicity of subdifferential mappings
• Subgradients of a convex function obtained from a directional derivative
• Approximate mean value theorem for upper subderivatives
• Subdifferential Determination of Essentially Directionally Smooth Functions in Banach Space
• On classes of subdifferentiability spaces of Ioffe
• Mean Value Property and Subdifferential Criteria for Lower Semicontinuous Functions
• First-order rules for nonsmooth constrained optimization

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