x = [ 0.55 0.0;
0.25 0.35
-0.2 0.2
-0.25 -0.1
-0.0 -0.3
0.4 -0.2 ]';
[n,m] = size(x);
cvx_begin
variable A(n,n) symmetric
variable b(n)
maximize( det_rootn( A ) )
subject to
norms( A * x + b * ones( 1, m ), 2 ) <= 1;
cvx_end
clf
noangles = 200;
angles = linspace( 0, 2 * pi, noangles );
ellipse = A \ [ cos(angles) - b(1) ; sin(angles) - b(2) ];
plot( x(1,:), x(2,:), 'ro', ellipse(1,:), ellipse(2,:), 'b-' );
axis off
Calling sedumi: 39 variables, 24 equality constraints
------------------------------------------------------------
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
Put 2 free variables in a quadratic cone
eqs m = 24, order n = 27, dim = 48, blocks = 10
nnz(A) = 66 + 0, nnz(ADA) = 354, nnz(L) = 189
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 1.05E+00 0.000
1 : 4.83E-02 3.88E-01 0.000 0.3694 0.9000 0.9000 3.93 1 1 8.7E-01
2 : -6.52E-01 1.49E-01 0.000 0.3837 0.9000 0.9000 1.02 1 1 4.1E-01
3 : -2.07E+00 4.01E-02 0.000 0.2693 0.9000 0.9000 0.22 1 1 1.7E-01
4 : -2.66E+00 2.82E-03 0.000 0.0703 0.9900 0.9900 0.83 1 1 1.3E-02
5 : -2.68E+00 5.87E-04 0.000 0.2083 0.9000 0.9000 1.00 1 1 2.7E-03
6 : -2.68E+00 2.73E-05 0.000 0.0465 0.9900 0.9900 1.00 1 1 1.4E-04
7 : -2.68E+00 7.85E-07 0.000 0.0287 0.9905 0.9900 1.00 1 1 1.0E-05
8 : -2.68E+00 1.91E-08 0.000 0.0243 0.9900 0.9820 1.00 1 1 2.4E-07
9 : -2.68E+00 3.95E-10 0.000 0.0207 0.9901 0.9900 1.00 2 2 5.2E-09
iter seconds digits c*x b*y
9 0.1 Inf -2.6839853868e+00 -2.6839853740e+00
|Ax-b| = 4.4e-09, [Ay-c]_+ = 2.6E-09, |x|= 1.0e+01, |y|= 2.5e+00
Detailed timing (sec)
Pre IPM Post
1.000E-02 5.000E-02 1.000E-02
Max-norms: ||b||=1, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 61.2392.
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +2.68399