We shall consider the optimal hyperplanes which minimize the sum of absolute deviations with respect to the m-dimensional data. Though similar problem was treated in the linear programming, we shall discuss the problem from algebraic viewpoint, and we shall show that the set
U of the coefficient vectors of all optimal hyperplanes of degree
m-1 becomes a bounded and closed convex cell in
Em. Further, we shall obtain a necessary and sufficient condition for the extreme point of
U, and then we establish a method for finding the set
U. Thus we find that the optimal set
U is completely determined as a hull of extreme points of
U. Finally, we shall apply these results to the numerical examples and determine their optimal sets.
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