The present invention applies a novel iterative algorithm to the problem of multidimensional optimization by supplying a strict, nonlinear mathematical solution to what has traditionally been treated as a linear multidimensional problem. The process consists of randomly selecting a statistically significant sample of a prospect list, calculating the value of the utility function for each pair of an offer and selected prospects, reducing the original linear multidimensional problem to a non-linear problem with a feasible number of dimensions, solving the non-linear problem for the selected sample numerically with the desired tolerance using an iterative algorithm, and using the results to calculate an optimal set of offers in one pass for the full prospect list.