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Dual characterizations of relative continuity of convex functions
Published online by Cambridge University Press: 09 April 2009
Abstract
Various properties of continuity for the class of lower semicontinuous convex functions are considered and dual characterizations are established. In particular, it is shown that the restriction of a lower semicontinuous convex function to its domain (respectively, domain of subdifferentiability) is continuous if and only if its subdifferential is strongly cyclically monotone (respectively, σ-cyclically monotone).
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- Copyright © Australian Mathematical Society 2001