Euclidean distance between polyhedra
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: 41 variables (10 free), 30 equality constraints
------------------------------------------------------------------------
SeDuMi 1.1 by AdvOL, 2005 and Jos F. Sturm, 1998, 2001-2003.
Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
Split 10 free variables
eqs m = 30, order n = 48, dim = 52, blocks = 2
nnz(A) = 300 + 0, nnz(ADA) = 600, nnz(L) = 315
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 9.10E-001 0.000
1 : 1.46E-001 4.20E-001 0.000 0.4609 0.9000 0.9000 3.17 1 1 1.5E+000
2 : 6.39E-001 1.14E-001 0.000 0.2726 0.9000 0.9000 1.85 1 1 2.9E-001
3 : 4.83E-001 3.04E-002 0.000 0.2656 0.9000 0.9000 1.31 1 1 7.7E-002
4 : 5.06E-001 2.68E-003 0.000 0.0884 0.9900 0.9900 1.09 1 1 6.8E-003
5 : 5.07E-001 1.00E-003 0.000 0.3737 0.9000 0.9000 1.02 1 1 2.7E-003
6 : 5.09E-001 2.51E-005 0.000 0.0250 0.9902 0.9900 1.01 1 1 7.5E-005
7 : 5.09E-001 4.24E-007 0.000 0.0169 0.9901 0.9900 1.00 1 1 1.4E-006
8 : 5.09E-001 3.72E-008 0.407 0.0877 0.9900 0.9900 1.00 1 1 1.3E-007
9 : 5.09E-001 1.15E-009 0.000 0.0310 0.9900 0.9737 1.00 1 1 4.0E-009
iter seconds digits c*x b*y
9 0.1 8.0 5.0856706332e-001 5.0856705866e-001
|Ax-b| = 1.6e-009, [Ay-c]_+ = 5.1E-010, |x|= 6.6e+000, |y|= 1.5e+000
Detailed timing (sec)
Pre IPM Post
0.000E+000 9.013E-002 0.000E+000
Max-norms: ||b||=2.829728e+000, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 2.11833.
------------------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +0.508567
------------------------------------------------------------------
The distance between the 2 polyhedra C and D is:
dist(C,D) = 0.50857