The Semiconvex Regularization of Functions

Methods involving semicontinuity and convergence; relaxation (49J45) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Duality theory (optimization) (49N15) Convexity of real functions of several variables, generalizations (26B25) Derivatives of functions in infinite-dimensional spaces (46G05) Calculus of functions on infinite-dimensional spaces (26E15)

Cites Work

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Subdifferentiation of regularized functions
Analysis. From concepts to applications
Approximation and regularization of arbitrary functions in Hilbert spaces by the Lasry-Lions method
Semiconcave functions, Hamilton-Jacobi equations, and optimal control
Approximately convex functions and approximately monotonic operators
Subdifferentials of distance functions, approximations and enlargements
Compensated convexity and its applications
A remark on regularization in Hilbert spaces
Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces
Problème d'optimisation defini par des fonctions qui sont sommes de fonctions convexes et de fonctions derivables
Helping you finding an appropriate regularization process
Uniformly convex and uniformly smooth convex functions
Regularity of quasiconvex envelopes
Differentiability of convex envelopes
Calculus Without Derivatives
Strong and Weak Convexity of Sets and Functions
Compensated Convexity Methods for Approximations and Interpolations of Sampled Functions in Euclidean Spaces: Theoretical Foundations
On the Smoothness of Convex Envelopes
Compensated Convexity, Multiscale Medial Axis Maps and Sharp Regularity of the Squared-Distance Function
Optimization and nonsmooth analysis
On α(·)-monotone multifunctions and differentiability of γ-paraconvex functions
Variational Analysis
What is the Subdifferential of the Closed Convex Hull of a Function?
On various semiconvex relaxations of the squared-distance function
Variational Analysis of Regular Mappings
The Bregman Proximal Average
A Proximal Average for Prox-Bounded Functions
Compensated convexity and Hausdorff stable geometric singularity extractions
Lower Semicontinuous Convex Relaxation in Optimization
Paraconvex functions and paraconvex sets
Proximité et dualité dans un espace hilbertien