On the Rockafellar theorem for $Φ^{γ(·,·)}$-monotone multifunctions

• Autorzy: S. Rolewicz
• Języki publikacji: EN

Abstrakty

EN

Let X be an arbitrary set, and γ: X × X → ℝ any function. Let Φ be a family of real-valued functions defined on X. Let $Γ: X → 2^{Φ}$ be a cyclic $Φ^{γ(·,·)}$-monotone multifunction with non-empty values. It is shown that the following generalization of the Rockafellar theorem holds. There is a function f: X → ℝ such that Γ is contained in the $Φ^{γ(·,·)}$-subdifferential of f, $Γ(x) ⊂ ∂_{Φ}^{γ(·,·)} f|_{x}$.

Kategorie tematyczne

• 26E15: Calculus of functions on infinite-dimensional spaces
• 52A01: Axiomatic and generalized convexity
• 46N10: Applications in optimization, convex analysis, mathematical programming, economics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 172
• Numer: 2
• Strony: 197-202

Daty

wydano

2006

Twórcy

autor

S. Rolewicz

• Institute of Mathematics, Polish Academy of Sciences, P.O. Box 21, Śniadeckich 8, 00-956 Warszawa, Poland

Identyfikatory

DOI

10.4064/sm172-2-6