Every closed convex set is the set of minimizers of some $C^{\infty }$-smooth convex function

DOI10.1090/S0002-9939-02-06695-9zbMath1028.49003OpenAlexW1778006028MaRDI QIDQ4547043

Daniel Azagra, Juan Ferrera

Publication date: 20 August 2002

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-02-06695-9

zbMATH Keywords

Hausdorff limitclosed convex setsMosco limitsmooth approximation of convex sets

Mathematics Subject Classification ID

Normed linear spaces and Banach spaces; Banach lattices (46B99) Convex functions and convex programs in convex geometry (52A41) Existence theories for problems in abstract spaces (49J27) Derivatives of functions in infinite-dimensional spaces (46G05)

Related Items (9)

Some new optimality conditions for semivector bilevel optimization program ⋮ Smooth convex extensions of convex functions ⋮ Random multifunctions as set minimizers of infinitely many differentiable random functions ⋮ Some remarks on the existence and computation of contingent epiderivatives ⋮ Robust MPC via min-max differential inequalities ⋮ \(L^{\infty}\) estimate for a limiting form of Ginzburg-Landau systems in convex domains ⋮ The 2D compressible Euler equations in bounded impermeable domains with corners ⋮ Stable conical regularization by constructible dilating cones with an application to \(L^{p}\)-constrained optimization problems ⋮ Unified framework for the propagation of continuous-time enclosures for parametric nonlinear ODEs

Cites Work

• Analytic and polyhedral approximation of convex bodies in separable polyhedral Banach spaces
• Smooth functions on \(c_0\)
• On smooth variational principles in Banach spaces
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