Title

Algebraic Core and Convex Calculus Without Topology

Published In

Optimization

Document Type

Citation

Publication Date

8-4-2020

Abstract

In this paper we study the concept of algebraic core for convex sets in general vector spaces without any topological structure and then present its applications to problems of convex analysis and optimization. Deriving the equivalence between the Hahn-Banach theorem and and a simple version of the separation theorem of convex sets in vector spaces allows us to develop a geometric approach to generalized differential calculus for convex sets, set-valued mappings, and extended-real-valued functions with qualification conditions formulated in terms of algebraic cores for such objects. We also obtain a precise formula for computing the subdifferential of optimal value functions associated with convex problems of parametric optimization in vector spaces. Functions of this type play a crucial role in many aspects of convex optimization and its applications.

Rights

Copyright © 2020 Informa UK Limited

DOI

10.1080/02331934.2020.1800700

Persistent Identifier

https://archives.pdx.edu/ds/psu/34231

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