Entropy Optimization Problems for Modified Verma Measures in Primal and Dual Spaces

In the present paper we formulate the dual problem for a primal problem concerned with the maximization of the modified version of Verma measure of entropy [1-2] or minimization of corresponding measure of cross-entropy. In this case, it is shown that the maximum value of that entropy (or minimum value of the corresponding cross-entropy, which is motivated by Kullback [3]-Leibler [4] is equal to the minimum (or maximum) value of the objective function of the dual problem. The recovery of the primal problem, when the dual problem is given, is also discussed.