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Chebyshev Center and Radius

Chebyshev Center and Radius

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Computes the Chebyshev center and Chebyshev radius of a polytope.

chebycenter(A,b)
function [c,r] = chebycenter(A,b)
%CHEBYCENTER Compute Chebyshev center of polytope Ax <= b.
%  The Chebyshev center of a polytope is the center of the largest
%  hypersphere enclosed by the polytope. 
%  Requires optimization toolbox.

[n,p] = size(A);
an = sqrt(sum(A.^2,2));
A1 = zeros(n,p+1);
A1(:,1:p) = A;
A1(:,p+1) = an;
f = zeros(p+1,1);
f(p+1) = -1;

options = optimset;
options = optimset(options,'Display', 'off');
c = linprog(f,A1,b,[],[],[],[],[],options);
r = c(p+1);
c = c(1:p);
end

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