Entropy Optimization Models with Convex Constraints

In this paper, we study the minimum cross-entropy optimization problem subject to a general class of convex constraints. Using a simple geometric inequality and the conjugate inequality we demonstrate how to directly construct a "partial" geometric dual program which allows us to apply the dual perturbation method to derive the strong duality theorem and a dual-to-primal conversion formula. This approach generalizes the previous results of linearly, quadratically, and entropically constrained cross-entropy optimization problems and provides a platform for using general purpose optimizers to generate ε-optimal solution pair to the problem.