两个多面体之交上的最佳逼近与保凸回归问题

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

本文提出了一种求Hilbert空间中给定点x0在两个多面体K’与K”之交上的最佳逼近的算法,它把问题化归为有限次求点在K’与K”中的最佳逼近的问题.由于保凸回归问题可表述为求某点x0在两个锐锥之交上的最佳逼近问题,故结合熟知的锐锥逼近的PAVA算法即可得到保凸回归的有限算法.文章还计算了一个保凸回归问题的实例.

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.