A weak* approximation of subgradient of convex function

• Autorzy: Zagrodny D.
• Języki publikacji: EN

Abstrakty

EN

Let [...] be a sequence of proper lower semicontinuous convex functions on a weakly compactly generated Banach space. Conditions ensuring the weak* convergence of their subgradients are given.

Słowa kluczowe

EN

subdifferentials; Attouch's theorem; Kronecker's lemma; Mosco convergence; convex functions; weakly compactly generated Banach spaces

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2007
• Tom: Vol. 36, no. 3
• Strony: 793--802
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Zagrodny D.

• Faculty of Mathematics and Natural Science, College of Science, Cardinal Stefan Wyszynski University, Dewajtis 5, 01-815 Warsaw, Poland

Bibliografia

• ATTOUCH, H. (1984) Variational Convergence for Functions and Operators. Pitman Advanced Publishing Program, Boston.
• ATTOUCH, H. and BEER, G. (1993) On the convergence of subdifferentials of convex functions. Arch. Math. 60, 389-400.
• BEER, G. and THERA, M. (1994) Attouch-Wets convergence and a differential operator for convex functions. Proc. Amer. Math. Soc. 122 (3), 851-860.
• COMBARI, C. and THIBAULT, L. (1998) On the graph convergence of subdifferentials of convex functions. Proc. Amer. Math. Soc. 126 (8), 2231-2240.
• JAJTE, R. (2003) On the strong law of large numbers. The Annals of Probability 31 (1), 409-412.
• MORICZ, F. (1982) Generalization of two theorems of Kronecker and of Knopp for multiple numerical series. Analysis 2, 49-64.
• PHELPS, R.R. (1984) Convex Functions, Monotone Operators and Differentiability. Springer-Verlag, Berlin.
• ROLEWICZ, S. (1984) Metric linear spaces (second edition). PWN, Warszawa.
• ZAGRODNY, D. (2005a) On the weak* convergence of subdifferentials of convex functions. J. Conv. Anal. 12 (1), 213-219.
• ZAGRODNY, D. (2005b) Minimizers of the limit of Mosco converging functions. Arch. Math. 85, 440-445.