A Representation Approach for Relative Entropy Minimization with Expectation Constraints

We consider the general problem of relative entropy minimization and entropy maximization subject to expectation constraints. We show that the solutions can be represented as members of an exponential family subject to weaker conditions than previously shown, and the representation can be simplified further if an appropriate conjugate prior density is used. As a result, the solutions can be found by optimization with respect to members of the parametric families corresponding to these representations.