Geodesic
Characterizations of Pointwise Additivity of Subdifferential
Journal of convex analysis, Tome 20 (2013) no. 1, pp. 221-231

Voir la notice de l'article provenant de la source Heldermann Verlag

We prove that the additivity of subdifferential in a given point of a locally convex space X is equivalent to other important optimality properties of an associated family of optimization problems. As a consequence, the subdifferential additivity is characterized by a dual closedness condition in X* × R, where R are the reals, endowed with the weak-star topology. Also, some special cases in which this closedness condition can be given in X* are presented.
Classification : 46N10, 26E15, 49J52, 52A41
Mots-clés : Lower-semicontinuous function, conjugate function, subdifferential, additivity of subdifferential, convolution, normal cone 
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     author = {T. Precupanu},
     title = {Characterizations of {Pointwise} {Additivity} of {Subdifferential}},
     journal = {Journal of convex analysis},
     pages = {221--231},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2013},
     url = {http://geodesic.mathdoc.fr/item/JCA_2013_20_1_JCA_2013_20_1_a12/}
}
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T. Precupanu. Characterizations of Pointwise Additivity of Subdifferential. Journal of convex analysis, Tome 20 (2013) no. 1, pp. 221-231. http://geodesic.mathdoc.fr/item/JCA_2013_20_1_JCA_2013_20_1_a12/