Maximum entropy of nonnegative functions subject to convex constraints
2013
In this paper we discuss the problem of maximizing the entropy of a nonnegative
function on a σ-finite measure space subject to convex constraints. For a finite
number of moment conditions, the search for an essential set reduces the problem to
a system of nonlinear equations. We also pose a finite dimensional dual optimization
problem whose solution is related to the solution of the primal problem. Finally
we provide an abstract unifying approach in order to include maximum entropy
problems when a finite number of marginals of a probability density are given.
Some illustrative examples are provided.
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