Approximation of the yolk by the LP yolk

If n points are sampled independently from an absolutely continuous distribution with support a convex subset of <2, then the center and radius of the ball determined by the bounding median lines (the LP yolk) converge with probability one to the center and radius of the yolk. The linear program of [9] is therefore an effective heuristic for computing the yolk in large samples. This result partially explains the results of numerical experiments in [8], where the bounding median lines always produced a radius within 2% of the yolk radius. ∗Research supported in part by National Science Foundation Grant #SES9011828 to the California Institute of Technology †Research supported by a Presidential Young Investigator Award from the National Science Foundation (ECS-8451032), and a Senior Research Associateship from the National Research Council ‡at the Naval Postgraduate School, Operations Research Department,Monterey CA, academic year 1990-1991