n = 2;
px = [0 .5 2 3 1];
py = [0 1 1.5 .5 -.5];
m = size(px,2);
pxint = sum(px)/m; pyint = sum(py)/m;
px = [px px(1)];
py = [py py(1)];
A = zeros(m,n); b = zeros(m,1);
for i=1:m
A(i,:) = null([px(i+1)-px(i) py(i+1)-py(i)])';
b(i) = A(i,:)*.5*[px(i+1)+px(i); py(i+1)+py(i)];
if A(i,:)*[pxint; pyint]-b(i)>0
A(i,:) = -A(i,:);
b(i) = -b(i);
end
end
cvx_begin
variable B(n,n) symmetric
variable d(n)
maximize( det_rootn( B ) )
subject to
for i = 1:m
norm( B*A(i,:)', 2 ) + A(i,:)*d <= b(i);
end
cvx_end
noangles = 200;
angles = linspace( 0, 2 * pi, noangles );
ellipse_inner = B * [ cos(angles) ; sin(angles) ] + d * ones( 1, noangles );
ellipse_outer = 2*B * [ cos(angles) ; sin(angles) ] + d * ones( 1, noangles );
clf
plot(px,py)
hold on
plot( ellipse_inner(1,:), ellipse_inner(2,:), 'r--' );
plot( ellipse_outer(1,:), ellipse_outer(2,:), 'r--' );
axis square
axis off
hold off
Calling sedumi: 34 variables, 15 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 = 15, order n = 23, dim = 42, blocks = 8
nnz(A) = 53 + 0, nnz(ADA) = 119, nnz(L) = 67
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 4.08E+00 0.000
1 : 1.21E+00 1.71E+00 0.000 0.4194 0.9000 0.9000 2.95 1 1 1.6E+00
2 : 6.35E-01 5.08E-01 0.000 0.2970 0.9000 0.9000 2.13 1 1 3.8E-01
3 : 8.84E-01 9.53E-02 0.000 0.1874 0.9000 0.9000 0.94 1 1 8.0E-02
4 : 9.48E-01 5.96E-03 0.000 0.0625 0.9900 0.9900 0.95 1 1 5.1E-03
5 : 9.52E-01 1.60E-04 0.000 0.0268 0.9900 0.9900 1.00 1 1 1.4E-04
6 : 9.52E-01 8.02E-06 0.372 0.0502 0.9904 0.9900 1.00 1 1 5.3E-06
7 : 9.52E-01 1.58E-06 0.000 0.1969 0.9120 0.9000 1.00 1 1 1.0E-06
8 : 9.52E-01 3.36E-07 0.121 0.2127 0.9168 0.9000 1.00 1 1 2.3E-07
9 : 9.52E-01 5.63E-08 0.000 0.1675 0.9096 0.9000 1.00 1 1 4.4E-08
10 : 9.52E-01 8.02E-09 0.000 0.1425 0.9101 0.9000 1.00 1 1 7.2E-09
iter seconds digits c*x b*y
10 0.1 8.1 9.5230751775e-01 9.5230750982e-01
|Ax-b| = 1.3e-10, [Ay-c]_+ = 4.2E-09, |x|= 2.2e+00, |y|= 2.6e+00
Detailed timing (sec)
Pre IPM Post
1.000E-02 9.000E-02 0.000E+00
Max-norms: ||b||=1, ||c|| = 2.474874e+00,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 1.03991.
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +0.952308