Determination of convex functions via subgradients of minimal norm

DOI10.1007/s10107-020-01550-wzbMath1482.26018OpenAlexW3048234810MaRDI QIDQ2235158

Emilio Vilches, Pedro Pérez-Aros, David Salas

Publication date: 20 October 2021

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10107-020-01550-w

zbMATH Keywords

Dirichlet boundary conditionslopeMoreau-Yosida approximationsubdifferential determinationsubgradient flows

Mathematics Subject Classification ID

Derivative-free methods and methods using generalized derivatives (90C56) Variational inequalities (49J40) Nonlinear differential equations in abstract spaces (34G20) Ordinary differential inclusions (34A60) Convexity of real functions of several variables, generalizations (26B25) Monotone systems involving ordinary differential equations (34C12)

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The slope robustly determines convex functions ⋮ Determining functions by slopes ⋮ Proximal determination of convex functions ⋮ Well-posedness of fractional Moreau's sweeping processes of Caputo type ⋮ Determination of functions by metric slopes

Cites Work

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• Global attractors for gradient flows in metric spaces
• Integration formulas via the Fenchel subdifferential of nonconvex functions
• Convex functions, monotone operators and differentiability
• Lower subdifferentiability and integration
• Links between functions and subdifferentials
• Integration of subdifferentials of lower semicontinuous functions on Banach spaces
• Stochastic subgradient method converges on tame functions
• Integration of primal lower nice functions in Hilbert spaces
• Characterization of the subdifferentials of convex functions
• Curves of Descent
• An Introduction to the Theory of Viscosity Solutions for First-Order Hamilton–Jacobi Equations and Applications
• Variational Analysis in Sobolev and BV Spaces
• Subdifferential Determination of Essentially Directionally Smooth Functions in Banach Space
• Integration of multivalued operators and cyclic submonotonicity
• Integration of subdifferentials of nonconvex functions
• Gradient Flows, Second-Order Gradient Systems and Convexity
• Variational Analysis of Regular Mappings
• Enlarged Inclusion of Subdifferentials
• Proximité et dualité dans un espace hilbertien
• On the Subdifferentiability of Convex Functions
• Convex analysis and monotone operator theory in Hilbert spaces