Vol. 33, No. 1, 1970

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On the maximal monotonicity of subdifferential mappings

Ralph Tyrrell Rockafellar

Vol. 33 (1970), No. 1, 209–216

The subdifferential of a lower semicontinuous proper convex function on a Banach space is a maximal monotone operator, as well as a maximal cyclically monotone operator. This result was announced by the author in a previous paper, but the argument given there was incomplete; the result is proved here by a different method, which is simpler in the case of reflexive Banach spaces. At the same time, a new fact is established about the relationship between the subdifferential of a convex function and the subdifferential of its conjugate in the nonreflexive case.

Mathematical Subject Classification
Primary: 46.45
Received: 17 July 1969
Published: 1 April 1970
Ralph Tyrrell Rockafellar