An analytical solution to the minimum Lp-norm of a hyperplane

[摘要] We consider in this paper the problem of determining the minimum L-p-norm of a hyperplane in n-dimensional space. A subset of the hyperplant is identified first that contains the optimal solution. On this reduced feasible space, the sets of optimal solutions for all values of p, 1 less than or equal to p less than or equal to infinity, are analytically derived. Several interesting mathematical properties of the optimal solution are presented. For p, 1 < p < infinity. It is proved that a unique solution exists, while for the limiting values p = 1, infinity, conditions on the equation coefficients of the hyperplane are found for which an infinite number of optimal solutions exist. The minimum L-p-distance of a point from a hyperplane is also analytically derived. (C) 1997 Academic Press.

[发布日期] 1997-07-01