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

Boris Mordukhovich; Dang Van Cuong; Gary Sandine; Nguyen Mau Nam

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arxiv 2201.10689 v2 pith:AAL6E3MI submitted 2022-01-26 math.OC

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 This is my paper

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keywords relativeconvexinteriortheoremdifferentiationgeneralizedgraphsqualifications

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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.

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

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