The least slope of a convex function and the maximal monotonicity of its subdifferential

DOI10.1007/BF00940043zbMath0795.49016OpenAlexW2107005342MaRDI QIDQ1321100

Stephen Simons

Publication date: 27 September 1994

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

Full work available at URL: https://doi.org/10.1007/bf00940043

zbMATH Keywords

subdifferentialsteepest descentseparation theoremsandwich theoremmaximal monotoneconvex lower- semicontinuous functionleast slope of a convex function

Mathematics Subject Classification ID

Nonsmooth analysis (49J52)

Related Items

Swimming below icebergs ⋮ Error bounds revisited ⋮ Subtangents with controlled slope ⋮ Subdifferential characterization of approximate convexity: The lower semicontinuous case ⋮ The maximal monotonicity of the subdifferentials of convex functions: Simons' problem ⋮ Mean Value Property and Subdifferential Criteria for Lower Semicontinuous Functions ⋮ Subdifferential estimate of the directional derivative, optimality criterion and separation principles ⋮ Bounded approximants to monotone operators on Banach spaces ⋮ Error bounds and metric subregularity ⋮ Subdifferentials are locally maximal monotone ⋮ Remarks on subgradients and \(\varepsilon\)-subgradients

Cites Work

• A note on epsilon-subgradients and maximal monotonicity
• Convex functions, monotone operators and differentiability
• On the maximal monotonicity of subdifferential mappings
• Subgradients of a convex function obtained from a directional derivative
• Optimization and nonsmooth analysis
• On the Identification of Active Constraints
• On the Subdifferentiability of Convex Functions