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arXiv · 2201.10689

Revisiting Rockafellar's Theorem on Relative Interiors of Convex Graphs with Applications to Convex Generalized Differentiation

Dang Van Cuong·Boris Mordukhovich·Nguyen Mau Nam·Gary Sandine
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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.

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Dang Van Cuong, Boris Mordukhovich, Nguyen Mau Nam, Gary Sandine. 2022-01-26. Revisiting Rockafellar's Theorem on Relative Interiors of Convex Graphs with Applications to Convex Generalized Differentiation. https://arxiv.org/abs/2201.10689

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