Section 4.3.1: Compute the Chebyshev center of a polyhedron
randn('state',0);
n = 10; m = 2*n;
A = randn(m,n);
b = A*rand(n,1) + 2*rand(m,1);
norm_ai = sum(A.^2,2).^(.5);
fprintf(1,'Computing Chebyshev center...');
cvx_begin
variable r(1)
variable x_c(n)
dual variable y
maximize ( r )
y: A*x_c + r*norm_ai <= b;
cvx_end
fprintf(1,'Done! \n');
fprintf(1,'The Chebyshev center coordinates are: \n');
disp(x_c);
fprintf(1,'The radius of the largest Euclidean ball is: \n');
disp(r);
Computing Chebyshev center...
Calling SeDuMi: 31 variables (11 free), 20 equality constraints
------------------------------------------------------------------------
SeDuMi 1.1 by AdvOL, 2005 and Jos F. Sturm, 1998, 2001-2003.
Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
Split 11 free variables
eqs m = 20, order n = 43, dim = 43, blocks = 1
nnz(A) = 460 + 0, nnz(ADA) = 400, nnz(L) = 210
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 6.02E-001 0.000
1 : -1.10E-002 1.22E-001 0.000 0.2022 0.9000 0.9000 1.00 1 1 2.0E+000
2 : -1.15E-001 3.91E-002 0.000 0.3218 0.9000 0.9000 2.70 1 1 9.1E-001
3 : -2.45E-001 1.07E-002 0.000 0.2739 0.9000 0.9000 1.93 1 1 8.2E-002
4 : -2.96E-001 2.98E-003 0.000 0.2776 0.9000 0.9000 1.03 1 1 2.0E-002
5 : -3.16E-001 8.64E-004 0.000 0.2903 0.9000 0.9000 1.08 1 1 5.1E-003
6 : -3.22E-001 4.31E-005 0.000 0.0499 0.9900 0.9900 1.21 1 1 2.3E-004
7 : -3.23E-001 1.67E-007 0.000 0.0039 0.9990 0.9990 1.06 1 1
iter seconds digits c*x b*y
7 0.1 Inf -3.2276133170e-001 -3.2276133170e-001
|Ax-b| = 6.1e-015, [Ay-c]_+ = 2.1E-016, |x|= 8.9e+000, |y|= 1.5e-001
Detailed timing (sec)
Pre IPM Post
0.000E+000 7.010E-002 0.000E+000
Max-norms: ||b||=4.197234e+000, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 1.51389.
------------------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +0.322761
Done!
The Chebyshev center coordinates are:
0.8511
-0.6874
1.1205
0.3555
0.2573
0.3947
1.1970
1.4711
1.7486
1.0573
The radius of the largest Euclidean ball is:
0.3228