  A closed convex polytope in n dimensions defined by m linear inequality
constraints is considered. If L is a straight line drawn in any direction from
any feasible point P, then in general, it intersects every constraint at one
point, giving m intersections. It is shown that there exists a unique feasible
point Q somewhere along this line, such that the sum of 1/di values is 0, where
di is the algebraic distance between Q and the intersection with constraint i,
measured along the line. The point Q is defined as the harmonic point along the
line L. The harmonic center of the polytope is defined as that point which is
the harmonic point for all n lines drawn through it, each parallel to one of
the coordinate axes. The existence and uniqueness of such a center is shown.
The harmonic center can be calculated using the coordinate search algorithm
(CS), as illustrated with some simple examples. The harmonic center defined
here is a generalization of the BI center defined earlier and is better in
several respects. It is shown that the harmonic center of the polytope is also
the harmonic point for any line drawn through it in any direction. It is also
shown that for any strictly feasible point P, there exists a unique harmonic
hyperplane passing through it, such that P is the harmonic point for any line
which lies in the harmonic hyperplane and passes through P.
