On cyclic α(·)-monotone multifunctions

• Autorzy: S. Rolewicz
• Języki publikacji: EN

Abstrakty

EN

Let (X,d) be a metric space. Let Φ be a linear family of real-valued functions defined on X. Let $Γ: X → 2^{Φ}$ be a maximal cyclic α(·)-monotone multifunction with non-empty values. We give a sufficient condition on α(·) and Φ for the following generalization of the Rockafellar theorem to hold. There is a function f on X, weakly Φ-convex with modulus α(·), such that Γ is the weak Φ-subdifferential of f with modulus α(·), $Γ(x)=∂^{-α}_{Φ}f|_{x}$.

Słowa kluczowe

EN

Fréchet Φ-differentiability; cyclic α(·)-monotone multi- function

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2000
• Tom: 141
• Numer: 3
• Strony: 263-272

Daty

wydano

2000

otrzymano

1999-09-07

otrzymano

2000-02-02

Twórcy

autor

S. Rolewicz

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 137, 00-950 Warszawa, Poland

Bibliografia

• R. Correa, A. Jofré and L. Thibault (1994), Subdifferential monotonicity as characterization of convex functions, Numer. Funct. Anal. Optim. 15, 531-535.
• A. Jourani (1996), Subdifferentiability and subdifferential monotonicity of γ-paraconvex functions, Control Cybernet. 25, 721-737.
• D. Pallaschke and S. Rolewicz (1997), Foundations of Mathematical Optimization, Math. Appl. 388, Kluwer, Dordrecht.
• R. T. Rockafellar (1970), On the maximal monotonicity of subdifferential mappings, Pacific J. Math. 33, 209-216.
• R. T. Rockafellar (1980), Generalized directional derivatives and subgradients of nonconvex functions, Canad. J. Math. 32, 257-280.
• S. Rolewicz (1999), On α(·)-monotone multifunctions and differentiability of γ-paraconvex functions, Studia Math. 133, 29-37.