Classification Schemes for Convex Conjugate Transform Dual Families.

By using the Ben Israel-Charnes-Kortanek classification theorem for convex sets, an analogous classification scheme is developed for convex conjugate transform dual families applicable to each of the equivalent problem formulations of Fenchel, Fockafellar, and Peterson, including the bifunctional representation. BCK duality states are introduced for convex conjugate problems, and it is determined which ones are possible and which are not. The classification theorem is valid for any paired real topological vector spaces having the Hahn-Banach extension property when any proper convex bifunction is specified. Author