
Journal of Convex Analysis 20 (2013), No. 1, 221231 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 weakstar topology. Also, some special cases in which this closedness condition can be given in X* are presented. Keywords: Lowersemicontinuous function, conjugate function, subdifferential, additivity of subdifferential, convolution, normal cone. MSC: 46N10, 26E15, 49J52, 52A41 [ Fulltextpdf (126 KB)] for subscribers only. 