Computational aspects of l-projections

The problem of finding the probability vector lying within a particular set e which minimizes the l-divergence between it and a specified probability vector r (the l-projection of r onto e) is often a difficult one. Here we establish a duality relationship between this problem and one of minimizing a linear combination of exponential functions. The latter problem is often much easier to solve. This fact coupled with a recent algorithm of Dykstra provides a new method of solving difficult l-projection problems. It is also shown that when e is a cone of isotonic vectors, the l-projection can be precisely expressed as a certain function of least squares equal weights projections.