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: 20 variables, 11 equality constraints
For improved efficiency, sedumi is solving the dual problem.
------------------------------------------------------------
SeDuMi 1.21 by AdvOL, 2005-2008 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
eqs m = 11, order n = 21, dim = 21, blocks = 1
nnz(A) = 220 + 0, nnz(ADA) = 121, nnz(L) = 66
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 1.53E+02 0.000
1 : -6.06E-01 3.12E+01 0.000 0.2043 0.9000 0.9000 1.15 1 1 2.1E+01
2 : -9.46E-03 9.65E+00 0.000 0.3093 0.9000 0.9000 2.65 1 1 3.1E+00
3 : 2.00E-01 3.30E+00 0.000 0.3422 0.9000 0.9000 1.53 1 1 1.1E+00
4 : 2.68E-01 8.55E-01 0.000 0.2588 0.9000 0.9000 1.11 1 1 2.9E-01
5 : 2.87E-01 2.97E-01 0.000 0.3480 0.9000 0.9000 0.85 1 1 1.3E-01
6 : 3.02E-01 1.42E-01 0.000 0.4782 0.9000 0.9000 -0.03 1 1 1.2E-01
7 : 3.24E-01 4.47E-02 0.000 0.3140 0.9000 0.9000 0.54 1 1 4.3E-02
8 : 3.33E-01 1.11E-02 0.000 0.2478 0.9000 0.9000 0.98 1 1 1.1E-02
9 : 3.36E-01 1.62E-03 0.000 0.1468 0.9167 0.9000 1.00 1 1 2.3E-03
10 : 3.37E-01 3.67E-05 0.000 0.0226 0.9901 0.9900 1.00 1 1
iter seconds digits c*x b*y
10 0.0 15.8 3.3705939820e-01 3.3705939820e-01
|Ax-b| = 1.8e-16, [Ay-c]_+ = 1.3E-15, |x|= 1.5e-01, |y|= 7.7e+00
Detailed timing (sec)
Pre IPM Post
1.000E-02 4.000E-02 0.000E+00
Max-norms: ||b||=1, ||c|| = 2.835687e+00,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 13.8708.
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +0.337059
Done!
The Chebyshev center coordinates are:
-0.1116
-1.5760
0.1079
-2.1751
3.2264
3.5820
4.3394
3.0680
0.4449
0.3164
The radius of the largest Euclidean ball is:
0.3371