Weak compactness and variational characterization of the convexity

DOI10.1007/s00009-012-0226-0zbMath1273.46057OpenAlexW2032699213MaRDI QIDQ1949857

Jean Saint Raymond

Publication date: 17 May 2013

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-012-0226-0

zbMATH Keywords

convex functionreflexive Banach spaceBanach spaceweak compactnessChebyshev setlower semi-continuous function

Mathematics Subject Classification ID

Convex functions and convex programs in convex geometry (52A41) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Duality and reflexivity in normed linear and Banach spaces (46B10)

Related Items (12)

One-sided James' compactness theorem ⋮ Weak compactness of sublevel sets in complete locally convex spaces ⋮ Unnamed Item ⋮ On a one-sided James' theorem ⋮ Conic James' Compactness Theorem ⋮ Compactness, Optimality, and Risk ⋮ On the range of the subdifferential in non reflexive Banach spaces ⋮ On the Klee--Saint Raymond's Characterization of Convexity ⋮ Mackey constraints for James's compactness theorem and risk measures ⋮ CHEBYSHEV SETS ⋮ Mixed variational formulations in locally convex spaces ⋮ Weak compactness of sublevel sets

Cites Work

• A coercive James's weak compactness theorem and nonlinear variational problems
• In a nonreflexive space the subdifferential is not onto
• Lebesgue property for convex risk measures on Orlicz spaces
• Differentiability Properties of Utility Functions
• Law invariant risk measures have the Fatou property
• ESSENTIAL SMOOTHNESS, ESSENTIAL STRICT CONVEXITY, AND LEGENDRE FUNCTIONS IN BANACH SPACES
• Weakly Compact Sets
• Unnamed Item
• Unnamed Item

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