Swimming below icebergs

DOI10.1007/BF01027109zbMath0807.46002OpenAlexW4234863992MaRDI QIDQ1332553

Stephen Simons

Publication date: 21 February 1995

Published in: Set-Valued Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01027109

zbMATH Keywords

Hahn-Banach theoremmaximal monotone operatorsubdifferentialsEkeland's variational principlemaximal monotonicitysublinear functionalbounded closed convex setsconvex lower surfacedirectional derivative of a convex functionepigraphs of proper convex lower semi-continuous functionsexistence of subtangentsRockafellar's maximal monotonicity theorem

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Set-valued operators (47H04) Geometry and structure of normed linear spaces (46B20) Theorems of Hahn-Banach type; extension and lifting of functionals and operators (46A22) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10) Derivatives of functions in infinite-dimensional spaces (46G05)

Related Items (3)

Constrained Equilibrium Point of Maximal Monotone Operator Via Variational Inequality ⋮ A strong mean value theorem and applications ⋮ The maximal monotonicity of the subdifferentials of convex functions: Simons' problem

Cites Work

• A note on epsilon-subgradients and maximal monotonicity
• Convex functions, monotone operators and differentiability
• The least slope of a convex function and the maximal monotonicity of its subdifferential
• Bounded approximants to monotone operators on Banach spaces
• On the maximal monotonicity of subdifferential mappings
• Subgradients of a convex function obtained from a directional derivative
• Approximate mean value theorem for upper subderivatives
• Subdifferentials are locally maximal monotone
• Nonconvex minimization problems
• The slice topology: a viable alternative to mosco convergence in nonreflexive spaces
• Subtangents with controlled slope
• On the Subdifferentiability of Convex Functions

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