Minimal antiderivatives and monotonicity
The authors study convex analytic frameworks which give rise to families of convex functions that contain their lower envelope. For a certain partial data regarding a subdifferential being given, they consider the family of all convex antiderivatives that comply with the given data. They prove that this family is non-empty and, specifically, contains a minimal antiderivative, in a rather general setting. Duality properties of representing functions are also captured, and the gap between the Fitzpatrick function and the Fitzpatrick family is filled by this notion of minimality of the Fitzpatrick function.
scientific article; zbMATH DE number 5810940