Extremal Principles and Optimization Dualities for Khinchin-Kullback-Leibler Estimation.
TEXAS UNIV AT AUSTIN CENTER FOR CYBERNETIC STUDIES
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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, 1 inequality attainment, 2 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.
- Statistics and Probability
- Operations Research