Abstract

We investigate the epigraphical convergence of slopes of lower semicontinuous convex functions on Asplund spaces. This type of convergence of slopes is compared to the Painlevé-Kuratowski convergence of subdifferentials. Both convergences are shown to be equivalent under mild conditions of compactness type.

Author information

Contact details are reproduced from the original publication and may be historical.

Pedro Pérez-Aros

Departamento de Ingeniería Matemática, Centro de Modelamiento Matemático, Universidad de Chile, Santiago, Chile

pperez@dim.uchile.cl

Keywords

  • Convex function
  • slope
  • convergence of slopes
  • subdifferential
  • convergence of subdifferentials

Mathematics Subject Classification

49J52; 47J22, 58E30

Suggested citation

P. Pérez-Aros, L. Thibault, D. Zagrodny. “Convergence of Slopes in Asplund Spaces.” Journal of Convex Analysis 32 (2025), No. 3, 661–680.

Copyright Heldermann Verlag 2025