Improving Convergence Rates of a Class of Algorithms

We consider a class of optimization problems in which the aim is to find an optimizing probability distribution or measure. Optimal designs are a particular example. Other examples include parameter estimation, stratified sampling and image processing. We search for an optimal distribution in a design space which is a discretization of a continuous space. To construct the optimizing distributions we use a class of multiplicative algorithms. We then develop strategies for constructing designs and investigate techniques for improving convergence rates by using the properties of the directional derivatives of the criterion function.