Second-order characterizations of convex and pseudoconvex functions

• Autorzy: Ginchev I. , Ivanov V. I.
• Języki publikacji: EN

Abstrakty

EN

The present paper gives characterizations of radially u.s.c. convex and pseudoconvex functions f: X —> R defined on a convex subset X of a real linear space E in terms of first and second-order upper Dini-directional derivatives. Observing that the property f radially u.s.c. does not require a topological structure of E, we draw the possibility to state our results for arbitrary real linear spaces. For convex functions we extend a theorem of Huang, Ng [10]. For pseudoconvex functions we generalize results of Diewert, Avriel, Zang [6] and Crouzeix [4]. While some known results on pseudoconvex functions are stated in global concepts (e.g. Komlosi [11]), we succeeded in realizing the task to confine to local concepts only.

Słowa kluczowe

EN

nonsmooth analysis; second-order Dini-directional derivatives; second-order characterizations of convex and pseudoconvex functions

PL

analiza nonsmooth; Dini-pochodne kierunkowe drugiego rzędu; charakterystyka drugiego rzędu funkcji wypukłych; charakterystyka drugiego rzędu funkcji pseudowypukłych

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2003
• Tom: Vol. 9, nr 2
• Strony: 261--273
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Ginchev I.

• Department of Mathematics Technical University of Varna 9010 Varna, Bulgaria

autor

Ivanov V. I.

• Department of Mathematics Technical University of Varna 9010 Varna, Bulgaria

Bibliografia

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