Finding a point that satisfies many linear inequalities
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
variable x(n)
minimize( sum( max( A*x - b, 0 ) ) )
cvx_end
nv = length( find( A*x > b ) );
fprintf(1,'\nFound an x that violates %d out of %d inequalities.\n',nv,m);
Starting with an infeasible set of 150 inequalities in 10 variables.
Calling SeDuMi: 310 variables (10 free), 150 equality constraints
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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 = 150, order n = 321, dim = 321, blocks = 1
nnz(A) = 300 + 3000, nnz(ADA) = 150, nnz(L) = 150
Handling 20 + 0 dense columns.
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 1.48E+002 0.000
1 : 2.77E+001 7.99E+001 0.000 0.5388 0.9000 0.9000 4.79 1 1 1.5E+000
2 : 3.28E+001 2.04E+001 0.000 0.2553 0.9000 0.9000 2.03 1 1 3.7E-001
3 : 3.69E+001 5.54E+000 0.000 0.2714 0.9000 0.9000 1.16 1 1 1.1E-001
4 : 3.82E+001 2.04E+000 0.000 0.3685 0.9000 0.9000 1.03 1 1 4.2E-002
5 : 3.87E+001 6.37E-001 0.000 0.3123 0.9000 0.9000 1.01 1 1 1.4E-002
6 : 3.89E+001 1.85E-001 0.000 0.2900 0.9000 0.9057 1.00 1 1 3.8E-003
7 : 3.89E+001 3.67E-002 0.000 0.1985 0.9061 0.9000 1.00 1 1 8.1E-004
8 : 3.89E+001 5.34E-003 0.000 0.1457 0.9253 0.9000 1.00 1 1 1.6E-004
9 : 3.89E+001 1.60E-003 0.000 0.2990 0.9000 0.9306 1.00 1 1 3.6E-005
10 : 3.89E+001 8.74E-005 0.000 0.0547 0.9902 0.9900 1.00 1 1 2.3E-006
11 : 3.89E+001 1.91E-008 0.000 0.0002 0.9999 0.9999 1.00 1 1
iter seconds digits c*x b*y
11 0.2 15.3 3.8916762959e+001 3.8916762959e+001
|Ax-b| = 1.3e-014, [Ay-c]_+ = 4.3E-015, |x|= 1.5e+001, |y|= 7.4e+000
Detailed timing (sec)
Pre IPM Post
0.000E+000 1.903E-001 0.000E+000
Max-norms: ||b||=3.073745e+000, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 1.
------------------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +38.9168
Found an x that violates 56 out of 150 inequalities.