Optimal scaling of balls and polyhedra

The concern is with solving as linear or convex quadratic programs special cases of the optimal containment and meet problems. The optimal containment or meet problem is that of finding the smallest scale of a set for which some translation contains a set or meets each element in a collection of sets, respectively. These sets are unions or intersections of cells where a cell is either a closed polyhedral convex set or a closed solid ball.This work was supported in part by the Department of Energy Contract DE-AC03-76-SF00326, PA No. DE-AT-03-76ER72018; National Science Foundation Grants MCS79-03145 and SOC78-16811; and the Army Research Office—Durham, Contract DAAG-29-78-G-0026.