Abstract :
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
