The Relaxation Method for Linear Inequalities

Abstract

Let A be a closed set of points in the n-dimensional euclidean space E_n. If p and p₁ are points of E_n such that 1.1 then p₁ is said to be point-wise closer than p to the set A. If p is such that there is no point p₁ which is point-wise closer than p to A, then p is called a closest point to the set A.