  The iterative proportional fitting procedure (IPFP) was introduced formally
by Deming and Stephan in 1940. For bivariate densities, this procedure has been
investigated by Kullback and R\"{u}schendorf. It is well known that the IPFP is
a sequence of successive I-projections onto sets of probability measures with
fixed marginals. However, when finding the I-projection onto the intersection
of arbitrary closed, convex sets (e.g., marginal stochastic orders), a sequence
of successive I-projections onto these sets may not lead to the actual
solution. Addressing this situation, we present a new iterative I-projection
algorithm. Under reasonable assumptions and using tools from Fenchel duality,
convergence of this algorithm to the true solution is shown. The cases of
infinite dimensional IPFP and marginal stochastic orders are worked out in this
context.
