Builds and solves a simple inequality-constrained linear program
echo on
n = 10;
A = randn(2*n,n);
b = randn(2*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;
cvx_end
echo off
n = 10;
A = randn(2*n,n);
b = randn(2*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;
cvx_end
Calling sedumi: 20 variables, 10 equality constraints
For improved efficiency, sedumi is solving the dual problem.
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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 = 10, order n = 21, dim = 21, blocks = 1
nnz(A) = 200 + 0, nnz(ADA) = 100, nnz(L) = 55
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 8.65E+00 0.000
1 : 2.40E+00 2.79E+00 0.000 0.3230 0.9000 0.9000 0.77 1 1 9.1E+00
2 : 1.34E+00 8.68E-01 0.000 0.3110 0.9000 0.9000 0.35 1 1 4.6E+00
3 : 3.31E-01 4.19E-02 0.000 0.0482 0.9900 0.9900 -0.60 1 1 3.9E+00
4 : 2.03E-01 8.51E-06 0.000 0.0002 0.9999 0.9999 -0.98 1 1
Dual infeasible, primal improving direction found.
iter seconds |Ax| [Ay]_+ |x| |y|
4 0.0 3.9e-15 1.8e-20 8.9e+00 1.2e-20
Detailed timing (sec)
Pre IPM Post
1.000E-02 1.000E-02 0.000E+00
Max-norms: ||b||=2.818197e+00, ||c|| = 2.154474e+00,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 1.
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Status: Infeasible
Optimal value (cvx_optval): +Inf
echo off