chebyshev_center.m
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chebyshev_center.m
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			% Section 4.3.1: Compute the Chebyshev center of a polyhedron
			% Boyd & Vandenberghe "Convex Optimization"
			% Jo?le Skaf - 08/16/05
			%
			% The goal is to find the largest Euclidean ball (i.e. its center and
			% radius) that lies in a polyhedron described by linear inequalites in this
			% fashion: P = {x : a_i'*x <= b_i, i=1,...,m}

			% Generate the data
			randn('state',0);
			n = 10; m = 2*n;
			A = randn(m,n);
			b = Arand(n,1) + 2rand(m,1);
			norm_ai = sum(A.^2,2).^(.5);

			% Build and execute model
			fprintf(1,'Computing Chebyshev center...');
			cvx_begin
			variable r(1)
			variable x_c(n)
			dual variable y
			maximize ( r )
			y: Ax_c + rnorm_ai <= b;
			cvx_end
			fprintf(1,'Done! \n');

			% Display results
			fprintf(1,'The Chebyshev center coordinates are: \n');
			disp(x_c);
			fprintf(1,'The radius of the largest Euclidean ball is: \n');
			disp(r);