MVT, Integration, and Monotonicity of a Generalized Subdifferential in Locally Convex Spaces

Rafael Correa; Abderrahim Hantoute; Pedro Pérez-Aros

Abstract

We extend Zagrodny's Mean Value Theorem (MVT) to the class of weakly lower semicontinuous epi-pointed functions defined in locally convex spaces. With this at hand we extend the integration of generalized subdifferentials and the characterization of convexity via the monotonicity of the subdifferential.

Author information

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

Rafael Correa

Universidad de O'Higgins, and: DIM-CMM, Universidad de Chile, Chile

rafael.correa@uoh.cl

Abderrahim Hantoute

Center for Mathematical Modeling, Universidad de Chile, Chile
and: Department of Mathematics, University of Alicante, Alicante, Spain

ahantoute@dim.uchile.cl

Pedro Pérez-Aros

Instituto de Ciencias de la Ingeniería, Universidad de O'Higgins, Chile

pedro.perez@uoh.cl

Keywords

Approximate Mean Value Theorem
integration of subdifferentials
monotonicity of the subdifferential
epi-pointed functions
generalized subdifferentials

Mathematics Subject Classification

49J53, 49J52

Suggested citation

R. Correa, A. Hantoute, P. Pérez-Aros. “MVT, Integration, and Monotonicity of a Generalized Subdifferential in Locally Convex Spaces.” Journal of Convex Analysis 27 (2020), No. 4, 1345–1362.