A Simple Duality Proof for Quadratically Constrained Entropy Functionals and Extension to Convex Constraints

In this paper, a simple proof of duality results is presented that was recently derived by Zhang and Brockett [SIAM J. Appl. Math., 47 (1987), pp. 871-885] for the problem of minimizing the Kullback-Liebler discrimination information measure subject to quadratic and linear inequality constraints. The proof is a direct and simple application of Lagrangian Duality Theory and is extended to a more general class of entropy optimization problems with composite convex constraints.