Constrained Kullback-Leibler Estimation; Generalized Cobb-Douglas Balance, and Unconstrained Convex Programming.

Abstract

In this paper the authors characterize completely the relationships of (1) a more general case than Kullback-Leibler estimation with finite discrete distribution and linear inequality constraints, (2) unconstrained minimization of a convex potential, or neg-utility function and (3) generalized Cobb-Douglas 'equilibrium' or 'accounting balance' equations. An exact duality pair characterization of the relevant class of extended geometric programming problems is obtained in place of the weaker necessary or sufficient conditions of Duffin, Peterson, and Zener. A new class of 'entropic' solutions for n-person characteristic function games is presented which has an equivalent unconstrained convex programming dual characterization.