n = 2;
A = eye(n);
b = zeros(n,1);
C = [2 1; -.5 1];
d = [-3; -3];
cvx_begin
variables x(n) y(n) w(n)
dual variables lam muu z
minimize ( norm(w,2) )
subject to
lam: square_pos( norm (A*x + b) ) <= 1;
muu: square_pos( norm (C*y + d) ) <= 1;
z: x - y == w;
cvx_end
t = (x + y)/2;
p=z;
p(1) = z(2); p(2) = -z(1);
c = linspace(-2,2,100);
q = repmat(t,1,length(c)) +p*c;
nopts = 1000;
angles = linspace(0,2*pi,nopts);
[u,v] = meshgrid([-2:0.01:4]);
z1 = (A(1,1)*u + A(1,2)*v + b(1)).^2 + (A(2,1)*u + A(2,2)*v + b(2)).^2;
z2 = (C(1,1)*u + C(1,2)*v + d(1)).^2 + (C(2,1)*u + C(2,2)*v + d(2)).^2;
contour(u,v,z1,[1 1]);
hold on;
contour(u,v,z2,[1 1]);
axis square
plot(x(1),x(2),'r+');
plot(y(1),y(2),'b+');
line([x(1) y(1)],[x(2) y(2)]);
plot(q(1,:),q(2,:),'k');
Calling sedumi: 21 variables, 8 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
eqs m = 8, order n = 17, dim = 24, blocks = 6
nnz(A) = 24 + 0, nnz(ADA) = 30, nnz(L) = 19
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 4.00E+00 0.000
1 : -5.32E-02 1.36E+00 0.000 0.3414 0.9000 0.9000 2.28 1 1 2.5E+00
2 : 1.06E+00 3.17E-01 0.000 0.2324 0.9000 0.9000 1.18 1 1 5.3E-01
3 : 1.19E+00 6.24E-02 0.000 0.1968 0.9000 0.9000 1.23 1 1 9.4E-02
4 : 1.19E+00 4.54E-04 0.000 0.0073 0.9990 0.9990 1.02 1 1 6.7E-04
5 : 1.19E+00 1.91E-05 0.000 0.0420 0.9900 0.9900 1.00 1 1 2.8E-05
6 : 1.19E+00 5.96E-07 0.000 0.0313 0.9901 0.9900 1.00 1 1 8.1E-07
7 : 1.19E+00 2.48E-08 0.466 0.0416 0.9900 0.9905 1.00 1 1 3.9E-08
8 : 1.19E+00 4.88E-09 0.000 0.1967 0.9009 0.9000 1.00 2 2 7.3E-09
iter seconds digits c*x b*y
8 0.1 8.3 1.1924413559e+00 1.1924413499e+00
|Ax-b| = 1.3e-08, [Ay-c]_+ = 0.0E+00, |x|= 3.9e+00, |y|= 1.7e+00
Detailed timing (sec)
Pre IPM Post
1.000E-02 1.000E-01 2.000E-02
Max-norms: ||b||=3, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 1.31165.
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +1.19244