An Analytical Solution to the Minimum L -Norm p of a Hyperplane

We consider in this paper the problem of determining the minimum Lp-norm of a hyperplane in n-dimensional space. A subset of the hyperplane is identified first that contains the optimal solution. On this reduced feasible space, the sets of optimal solutions for all values of p, 1FpF`, are analytically derived. Several interesting mathematical properties of the optimal solution are presented. For p, 1-p-`, it is proved that a unique solution exists, while for the limiting values ps1, `, conditions on the equation coefficients of the hyperplane are found for which an infinite number of optimal solutions exist. The minimum Lp-distance of a point from a hyperplane is also analytically derived