Subdifferentiation of regularized functions

DOI10.1007/s11228-016-0367-6zbMath1334.49053OpenAlexW4301461342MaRDI QIDQ255190

Huynh Van Ngai, Jean-Paul Penot

Publication date: 9 March 2016

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

Full work available at URL: https://doi.org/10.1007/s11228-016-0367-6

zbMATH Keywords

monotonicitynonsmooth analysisregularizationconvolutionsubdifferentialsapproximately convex functions

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Continuous and differentiable maps in nonlinear functional analysis (46T20)

Related Items

Helping you finding an appropriate regularization process ⋮ Optimization conditions and decomposable algorithms for convertible nonconvex optimization ⋮ Subdifferentiation of integral functionals ⋮ The Semiconvex Regularization of Functions ⋮ A generalization of the Moreau-Yosida regularization ⋮ On proximal mappings with Young functions in uniformly convex Banach spaces ⋮ Well-posedness and subdifferentials of optimal value and infimal convolution

Cites Work

• Regularization of differential variational inequalities with locally prox-regular sets
• Primal-lower-nice property of value functions in optimization and control problems
• Metric projection and compatibly parameterized families of prox-regular sets in Hilbert space
• Approximation and regularization of arbitrary functions in Hilbert spaces by the Lasry-Lions method
• Convex functions, monotone operators and differentiability.
• Uniform prox-regularity of functions and epigraphs in Hilbert spaces
• Approximately convex functions and approximately monotonic operators
• A remark on regularization in Hilbert spaces
• Towards minimal assumptions for the infimal convolution regularization
• Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces
• Geometry of Banach spaces. Selected topics
• Proximal mappings
• Limit superior of subdifferentials of uniformly convergent functions
• Approximate convexity and submonotonicity.
• Reconstruction of the Clarke subdifferential by the Lasry-Lions regularizations
• Prox-regular functions in Hilbert spaces
• Integration of subdifferentials of lower semicontinuous functions on Banach spaces
• On the variational principle
• Prox-regularity of functions and sets in Banach spaces
• Metric regularity and subdifferential calculus in Banach spaces
• Differential properties of the Moreau envelope
• Softness, sleekness and regularity properties in nonsmooth analysis
• Integration of primal lower nice functions in Hilbert spaces
• Techniques of variational analysis
• Fréchet differentiability of convex functions
• On the Yosida approximation of operators
• Calculus Without Derivatives
• C ^{1,ω (·)} -regularity and Lipschitz-like properties of subdifferential
• Prox-regular sets and epigraphs in uniformly convex Banach spaces: Various regularities and other properties
• Strong and Weak Convexity of Sets and Functions
• Functional Analysis, Calculus of Variations and Optimal Control
• Integration of multivalued operators and cyclic submonotonicity
• Subsmooth sets: Functional characterizations and related concepts
• Calmness and Stability Properties of Marginal and Performance Functions
• Subdifferentiability spaces and nonsmooth analysis
• Evolution equations with lack of convexity
• Optimization and nonsmooth analysis
• The Proximal Normal Formula in Banach Space
• Existence Of Nearest Points In Banach Spaces
• Submonotone Subdifferentials of Lipschitz Functions
• Integration of subdifferentials of nonconvex functions
• An Extension of Attouch's Theorem and Its Application to Second-Order Epi-Differentiation of Convexly Composite Functions
• Convergence of Subdifferentials of Convexly Composite Functions
• Sub differential Monotonicity as Characterization of Convex Functions
• Local differentiability of distance functions
• On the coincidence of some subdifferentials in the class of α(.)-paraconvex functions
• Differentiability Properties of Optimal Value Functions
• Partial Extensions of Attouch's Theorem with Applications to Proto- Derivatives of Subgradient Mappings
• Nonsmooth sequential analysis in Asplund spaces
• Proximal Analysis and Approximate Subdifferentials
• Paraconvex functions and paraconvex sets
• Proximité et dualité dans un espace hilbertien
• Primal Lower Nice Functions and Their Moreau Envelopes
• Set-valued analysis
• Metric inequality, subdifferential calculus and applications
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item