Best Approximation from Intersection of Two Polyhedrons and Its Application in Convex Regression

Suppose K is the intersection of two polyhedrons K'and K" in a Hilbert space. This paper gives an algorithm for the best approximation to a given x from K, which reduces the problem to finite times of computing the best approximations from the individual K’ or K". Since by PAV Algorithm it is easy to get the best approximation to any x from an acute cone, and the problem of convex regression can be rewritten as an approximation problem from the intersection of two acute cones, by our algorithm the problem of convex regression is solved.