m = 150;
n = 10;
seed = 0;
randn('state',seed);
A = randn(m,n);
b = randn(m,1);
fprintf(1, ['Starting with an infeasible set of %d inequalities ' ...
'in %d variables.\n'],m,n);
cvx_begin
variables lambda(m)
minimize( sum( lambda ) )
subject to
A'*lambda == 0;
b'*lambda == -1;
lambda >= 0;
cvx_end
infeas_set = find( abs(b.*lambda) > sqrt(eps)/n );
disp(' ');
fprintf(1,'Found a smaller set of %d mutually inconsistent inequalities.\n',...
length(infeas_set));
disp(' ');
disp('A smaller set of mutually inconsistent inequalities are the ones');
disp('with row indices:'), infeas_set'
Starting with an infeasible set of 150 inequalities in 10 variables.
Calling sedumi: 150 variables, 11 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 = 11, order n = 151, dim = 151, blocks = 1
nnz(A) = 1650 + 0, nnz(ADA) = 121, nnz(L) = 66
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 2.27E+02 0.000
1 : 1.27E-02 7.71E+00 0.000 0.0339 0.9900 0.9900 2.93 1 1 1.7E+00
2 : 4.31E-01 2.34E+00 0.000 0.3028 0.9000 0.9000 0.88 1 1 8.0E-01
3 : 5.11E-01 1.16E+00 0.000 0.4971 0.9000 0.9000 0.88 1 1 5.3E-01
4 : 5.53E-01 4.79E-01 0.000 0.4126 0.9000 0.9000 0.95 1 1 2.9E-01
5 : 5.86E-01 1.85E-01 0.000 0.3860 0.9000 0.9000 0.95 1 1 1.4E-01
6 : 5.96E-01 7.30E-02 0.000 0.3946 0.9000 0.9125 0.99 1 1 6.2E-02
7 : 5.99E-01 2.74E-02 0.000 0.3748 0.9000 0.9202 1.00 1 1 2.6E-02
8 : 6.01E-01 7.80E-03 0.000 0.2850 0.9105 0.9000 1.00 1 1 7.4E-03
9 : 6.01E-01 4.39E-04 0.000 0.0563 0.9902 0.9900 1.00 1 1 4.2E-04
10 : 6.01E-01 5.09E-07 0.000 0.0012 0.9990 0.9990 1.00 1 1
iter seconds digits c*x b*y
10 0.0 Inf 6.0131198034e-01 6.0131198034e-01
|Ax-b| = 7.1e-17, [Ay-c]_+ = 1.3E-16, |x|= 2.8e-01, |y|= 8.1e-01
Detailed timing (sec)
Pre IPM Post
0.000E+00 4.000E-02 0.000E+00
Max-norms: ||b||=1, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 9.91492.
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +0.601312
Found a smaller set of 11 mutually inconsistent inequalities.
A smaller set of mutually inconsistent inequalities are the ones
with row indices:
ans =
1 22 33 54 59 73 79 94 115 136 149