Vol. 39, No. 2, 1971

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Integrals which are convex functionals. II

Ralph Tyrrell Rockafellar

Vol. 39 (1971), No. 2, 439–469
Abstract

Formulas are derived in this paper for the conjugates of convex integral functionals on Banach spaces of measurable or continuous vector-valued functions. These formulas imply the weak compactness of certain convex sets of summable functions, and they thus have applications in the existence theory and duality theory for various optimization problems. They also yield formulas for the subdifferentials of integral functionals, as well as characterizations of supporting hyperplanes and normal cones.

Mathematical Subject Classification 2000
Primary: 46E30
Secondary: 46G99, 28A30
Milestones
Received: 1 October 1969
Revised: 2 November 1970
Published: 1 November 1971
Authors
Ralph Tyrrell Rockafellar