Optimal design with bounded density: optimization algorithms of the exchange type

This paper deals with the design problem, initiated by Wynn (1982), arising in sampling experiments, experiments with the spatially distributed observations, or containing time type variables. The peculiarity of these experiments is that the number of observations in any given element of the design space cannot exceed some a priori prescribed level. In terms of the continous designs, this means that the density of design measure is restricted. The proposed algorithms are based on the simple heuristic idea: to delete, at every step of the iterative procedure, ‘bad’ (less informative) sets of the supporting points and to include ‘good’ (most informative) ones in the design. The convergence of the algorithm and its various modifications are the main topic of this paper