Revisiting Rockafellar's Theorem on Relative Interiors of Convex Graphs with Applications to Convex Generalized Differentiation
Optimization and Control
2023-04-06 v2
Abstract
In this paper we revisit a theorem by Rockafellar on representing the relative interior of the graph of a convex set-valued mapping in terms of the relative interior of its domain and function values. Then we apply this theorem to provide a simple way to prove many calculus rules of generalized differentiation of set-valued mappings and nonsmooth functions in finite dimensions. These results improve upon those in [14] by replacing the relative interior qualifications on graphs with qualifications on domains and/or ranges.
Keywords
Cite
@article{arxiv.2201.10689,
title = {Revisiting Rockafellar's Theorem on Relative Interiors of Convex Graphs with Applications to Convex Generalized Differentiation},
author = {Dang Van Cuong and Boris Mordukhovich and Nguyen Mau Nam and Gary Sandine},
journal= {arXiv preprint arXiv:2201.10689},
year = {2023}
}