Stochastic variants of the entropy programming

The first part of this paper presents the entropy programming problem and its duality results. The entropy programming is to find a non-negative vector the divergence of which from a given positive vector should be minimal supposing linear constraints. The measure of the divergence between two non-negative vectors is the generalization of the Kullbach-Leibler information. The main part of this paper presents two applications of this problem. Consider the transportation problem where some constraints are not required to be exactly satisfied rather the above divergence of the two sides is put into the objective function such a way that the weighted average of the original and the divergence should be minimal. Then the paper applies the entropy programming problem to the gravity model for trip distribution. Similarly to the above case it puts some constraints into the objective. Efficient algorithms were developed for the above problems, these algorithms have very good convergence properties.