Exact calculus for s-Holder subgradients in Banach spaces

  • Abdelaziz Haddane
  • Jamal Hlal University Mohammed I
  • Abdelhaq Benbrik University Mohammed I

Resumen

We give in this paper some useful calculus results related to the s-H$\ddot{o}$lder subdifferential of extended-real valued functions defined on arbitrary real Banach spaces.

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Biografía del autor/a

Abdelaziz Haddane

Department of Mathematics

Jamal Hlal, University Mohammed I

Department of Mathematics

Abdelhaq Benbrik, University Mohammed I

Department of Mathematics

Citas

Bernicot. F and Venel. J: Differential inclusions with proximal normal cones in Banach spaces, Journal of Convex Analysis, vol 17, no. 2, pp, 451-484, (2010).

Borwein, J. M and Press. D:A smooth variational principle with applications to subdifferentiability and to differentiability of convex functions. trans. Amer. Math. Soc. 303, 517-527. (1987).

Borwein, J. M, Girgensohn. R and Wang. X : On the Construction of Hölder and Proximal Subderivatives.www.cecm. cfu. ca.(1997).

Borwein, J. M, and Warren B. M and Wang. X: Lipschitz functions with prescribed derivatives and subderivatives, Nonlinear Analysis, Theory, Methods and Applications, vol. 29, no. 1, pg. 53-63, (1997).

Ioffe. A. D: Proximal analysis and approximate subdifferentials, J. London. Math. Soc. 41, 175-192, (1990).

Mordukhovich B. S: Maximum principle in the problem of time optimal response with nonsmooth contraints, Journal of Applied Mathematics and Méchanics, 40, 960-969, (1976).

Mordukhovich B. S and Y. Shao: On Nonconvex Subdifferential Calculus in Banach Spaces. Journal of Convex Analysis. Volume 2, 211-227, (1995).

Mordukovitch B. S and Nguyen M. N: Exact calculus for proximal subgradients with applications to optimization. ESAIM: PROCEEDINGS, Vol.17, 80-85. (2007).

Mordukovitch, B. S: Variational Analysis and Applications, Springer Monographs in Mathematics. Book, ISBN 978-3-319-92773-2. (2018).

Pawel. G and Sterm. R. J: Subdifferential analysis of the Van der Waerden function. Journal of Convex Analysis, vol 18, no. 3, pp, 451-484, (2011).

Zheng. X. Y and Kung. F. N : Hölder stable minimizers, tilt stability, and Hölder metric regularity of subdifferentials. SIAM J. OPTIM. Vol. 25, No. 1, pp. 416–438, (2015).

Publicado
2024-05-24
Sección
Articles