Journal of Convex Analysis 20 (2013), No. 1, 221--231
Copyright Heldermann Verlag 2013
Characterizations of Pointwise Additivity of Subdifferential
Teodor Precupanu
Dept. of Mathematics, University "Al. I. Cuza", Bd. Carol 11, 700506 Iasi, Romania
tprecup@uaic.ro
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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