Builds and solves a simple linear program
echo on
n = 100;
A = randn(0.5*n,n);
b = randn(0.5*n,1);
c = randn(n,1);
d = randn;
cvx_begin
variable x(n)
dual variables y z
minimize( c' * x + d )
subject to
y : A * x == b;
z : x >= 0;
cvx_end
echo off
Calling SeDuMi: 100 variables (0 free), 50 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
eqs m = 50, order n = 101, dim = 101, blocks = 1
nnz(A) = 5000 + 0, nnz(ADA) = 2500, nnz(L) = 1275
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 5.89E+000 0.000
1 : -3.33E+000 2.20E+000 0.000 0.3738 0.9000 0.9000 0.59 1 1 2.6E+001
2 : -3.04E+000 8.57E-001 0.000 0.3892 0.9000 0.9000 0.90 1 1 1.3E+001
3 : -3.11E+000 2.05E-001 0.000 0.2393 0.9000 0.9000 0.07 1 1 6.5E+000
4 : -3.01E+000 6.67E-003 0.000 0.0325 0.9900 0.9900 -0.72 1 1 6.1E+000
5 : -2.91E+000 1.54E-007 0.000 0.0000 1.0000 1.0000 -0.99 1 1
Dual infeasible, primal improving direction found.
iter seconds |Ax| [Ay]_+ |x| |y|
5 0.0 6.7e-014 8.3e-021 3.1e+001 9.4e-021
Detailed timing (sec)
Pre IPM Post
3.004E-002 4.006E-002 0.000E+000
Max-norms: ||b||=3.633265e+000, ||c|| = 3.486412e+000,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 1.
------------------------------------------------------------------------
Status: Unbounded
Optimal value (cvx_optval): -Inf