Extremal principles and optimization dualities for khinchin-kullback-leibler estimation

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Abstract
This paper presents a new extremal approach to deriving dual optimization problems with proper duality inequality which simplifies, and generalizes the Fenchel-Rockafellar scheme. Our derivation proceeds in two stages, (i) inequality attainment,(ii) decoupling primal and dual variables, The power and convenience of this approach are exhibited through a new, much simpler derivation of the Charnes-Cooper results for Khinchin-Kullback-Leibler statistical estimation [1], the immediate establishment of the C2 duality for general distributions and its extensions to general linear inequality constraints, plus the development of a new two-person zero-sum game connection.

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