Geodesic
Revisiting Rockafellar's Theorem on Relative Interiors of Convex Graphs with Applications to Convex Generalized Differentiation
Journal of convex analysis, Tome 30 (2023) no. 3, pp. 835-85
Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

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 for set-valued mappings and nonsmooth functions in finite dimensions. Using this important theorem by Rockafellar allows us to improve some results on generalized differentiation of set-valued mappings of B. S. Mordukhovich and N. M. Nam [Geometric approach to convex subdifferential calculus, Optimization 66 (2017) 839--873] by replacing the relative interior qualifications on graphs with qualifications on domains and/or ranges.
Classification : 49J52, 49J53, 90C31
Mots-clés : Convex analysis, generalized differentiation, geometric approach, relative interior, normal cone, subdifferential, coderivative, calculus rules 
@article{JCA_2023_30_3_JCA_2023_30_3_a3,
     author = {D. V. Cuong and B. S. Mordukhovich and N. M. Nam and G. Sandine},
     title = {Revisiting {Rockafellar's} {Theorem} on {Relative} {Interiors} of {Convex} {Graphs} with {Applications} to {Convex} {Generalized} {Differentiation}},
     journal = {Journal of convex analysis},
     pages = {835--85},
     year = {2023},
     volume = {30},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2023_30_3_JCA_2023_30_3_a3/}
}
TY  - JOUR
AU  - D. V. Cuong
AU  - B. S. Mordukhovich
AU  - N. M. Nam
AU  - G. Sandine
TI  - Revisiting Rockafellar's Theorem on Relative Interiors of Convex Graphs with Applications to Convex Generalized Differentiation
JO  - Journal of convex analysis
PY  - 2023
SP  - 835
EP  - 85
VL  - 30
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JCA_2023_30_3_JCA_2023_30_3_a3/
ID  - JCA_2023_30_3_JCA_2023_30_3_a3
ER  - 
%0 Journal Article
%A D. V. Cuong
%A B. S. Mordukhovich
%A N. M. Nam
%A G. Sandine
%T Revisiting Rockafellar's Theorem on Relative Interiors of Convex Graphs with Applications to Convex Generalized Differentiation
%J Journal of convex analysis
%D 2023
%P 835-85
%V 30
%N 3
%U http://geodesic.mathdoc.fr/item/JCA_2023_30_3_JCA_2023_30_3_a3/
%F JCA_2023_30_3_JCA_2023_30_3_a3
D. V. Cuong; B. S. Mordukhovich; N. M. Nam; G. Sandine. Revisiting Rockafellar's Theorem on Relative Interiors of Convex Graphs with Applications to Convex Generalized Differentiation. Journal of convex analysis, Tome 30 (2023) no. 3, pp. 835-85. http://geodesic.mathdoc.fr/item/JCA_2023_30_3_JCA_2023_30_3_a3/