Nonsmooth analysis on partially ordered vector spaces. I. Convex case

Nikolaos S. Papageorgiou

Vol. 107 (1983), No. 2, 403–458

DOI: 10.2140/pjm.1983.107.403

Abstract

Convex analysis provides the tools to extend results of differential calculus to nonsmooth real valued functions. The purpose of this article is to study those extensions for convex vector valued mappings. We study their continuity properties, develop a subdifferential calculus and a duality theory, similar to the one existing for real valued functions. We conclude with some useful deconvexification results.

Mathematical Subject Classification 2000

Primary: 47B55, 47B55

Secondary: 58C20, 49A50

Milestones

Received: 30 October 1981

Published: 1 August 1983