Characterizations of convex approximate subdifferential calculus in Banach spaces

DOI10.1090/tran/6589zbMath1336.49018OpenAlexW2212477482MaRDI QIDQ2790639

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Publication date: 7 March 2016

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/tran/6589

zbMATH Keywords

convex functionsinf-convolutionFenchel conjugatecalculus rulesapproximate subdifferentialapproximate variational principleMoreau-Yosida envelope

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Set-valued and variational analysis (49J53) Convex functions and convex programs in convex geometry (52A41) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10)

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Sequential \(\varepsilon\)-subdifferential calculus for scalar and vector mappings ⋮ Weaker conditions for subdifferential calculus of convex functions ⋮ Hiriart-Urruty-Phelps-like formula for the subdifferential of integral sums ⋮ Unnamed Item ⋮ Visualization of the \(\varepsilon \)-subdifferential of piecewise linear-quadratic functions

Cites Work

• On the convergence of subdifferentials of convex functions
• Limit superior of subdifferentials of uniformly convergent functions
• Subdifferential calculus using \(\varepsilon\)-subdifferentials
• Continuity of usual operations and variational convergences
• Stability results for convergence of convex sets and functions in nonreflexive spaces
• On the maximal monotonicity of subdifferential mappings
• Banach space theory. The basis for linear and nonlinear analysis
• Epi/Hypo–Convergence: The Slice Topology and Saddle Points Approximation
• Subdifferential Calculus Rules in Convex Analysis: A Unifying Approach Via Pointwise Supremum Functions
• Preservation of Convergence of Convex Sets and Functions in Finite Dimensions
• The slice topology: a viable alternative to mosco convergence in nonreflexive spaces
• Attouch-Wets Convergence and a Differential Operator for Convex Functions
• Sequential Convex Subdifferential Calculus and Sequential Lagrange Multipliers
• On the graph convergence of subdifferentials of convex functions
• Subdifferential calculus without qualification conditions, using approximate subdifferentials: A survey
• Operations on convergent families of sets and functions
• Set-valued analysis
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