Journal of Convex Analysis 20 (2013), No. 1, 221--231
Copyright Heldermann Verlag 2013
Characterizations of Pointwise Additivity of Subdifferential
Dept. of Mathematics, University "Al. I. Cuza", Bd. Carol 11, 700506 Iasi, Romania
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.
Keywords: Lower-semicontinuous function, conjugate function, subdifferential, additivity of subdifferential, convolution, normal cone.
MSC: 46N10, 26E15, 49J52, 52A41
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