An Analytical Solution to the MinimumLp-Norm of a Hyperplane

✍ Scribed by Emanuel Melachrinoudis

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 236 KB
• Volume: 211
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1997.5453

✦ Synopsis

We consider in this paper the problem of determining the minimum L -norm of p 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, 1 F p F ϱ, are analytically derived. Several interesting mathematical properties of the optimal solution are presented. For p, 1p -ϱ, it is proved that a unique solution exists, while for the limiting values p s 1, ϱ, conditions on the equation coefficients of the hyperplane are found for which an infinite number of optimal solutions exist. The minimum L -distance of a p point from a hyperplane is also analytically derived.