randn('state',0);
rand('state',0);
n = 5;
m1 = 2*n;
m2 = 3*n;
A1 = randn(m1,n);
A2 = randn(m2,n);
b1 = rand(m1,1);
b2 = rand(m2,1) + A2*randn(n,1);
cvx_begin
variables x(n) y(n)
minimize (norm(x - y))
A1*x <= b1;
A2*y <= b2;
cvx_end
disp('------------------------------------------------------------------');
disp('The distance between the 2 polyhedra C and D is: ' );
disp(['dist(C,D) = ' num2str(cvx_optval)]);
Calling sedumi: 31 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 = 28, dim = 32, blocks = 2
nnz(A) = 136 + 0, nnz(ADA) = 121, nnz(L) = 66
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 1.15E+01 0.000
1 : 3.14E-02 5.51E+00 0.000 0.4801 0.9000 0.9000 3.34 1 1 3.4E+00
2 : -5.66E-01 1.54E+00 0.000 0.2799 0.9000 0.9000 1.86 1 1 1.2E+00
3 : -4.73E-01 4.06E-01 0.000 0.2631 0.9000 0.9000 1.31 1 1 2.9E-01
4 : -5.06E-01 3.42E-02 0.000 0.0843 0.9900 0.9900 1.09 1 1 2.3E-02
5 : -5.07E-01 1.24E-02 0.000 0.3638 0.9000 0.9000 1.03 1 1 8.3E-03
6 : -5.08E-01 3.13E-04 0.000 0.0252 0.9900 0.8509 1.01 1 1 2.9E-04
7 : -5.09E-01 2.63E-06 0.286 0.0084 0.9990 0.9931 1.00 1 1 2.4E-06
8 : -5.09E-01 6.39E-09 0.248 0.0024 0.9990 0.9990 1.00 1 1 9.2E-09
iter seconds digits c*x b*y
8 0.0 Inf -5.0856705170e-01 -5.0856704680e-01
|Ax-b| = 2.1e-09, [Ay-c]_+ = 9.2E-09, |x|= 1.8e+00, |y|= 1.7e+00
Detailed timing (sec)
Pre IPM Post
1.000E-02 4.000E-02 1.000E-02
Max-norms: ||b||=1, ||c|| = 2.829728e+00,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 48.6227.
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +0.508567
------------------------------------------------------------------
The distance between the 2 polyhedra C and D is:
dist(C,D) = 0.50857