Abstract: A method for tracking objects is disclosed. First a region containing the objects is scanned to generate a multiplicity of sequential images or data sets of the region. A plurality of points in each of the images or data sets corresponds to a respective plurality of the objects. Next, respective figures of merit are determined for assigning the points to the tracks. Next, a k-dimensional cost function is defined which sums the figures of merit for combinations of assignments from the images or data sets. Next, the complexity of the cost function is reduced by Lagrangian Relaxation by permitting a point to be assigned to more than one track and adding a penalty factor to the cost function when a point is assigned to more than one track. The reducing step is iteratively repeated and the resultant penalized cost function is solved.