Builds and solves a simple least-squares problem using cvx
echo on
n = 100;
A = randn(2*n,n);
b = randn(2*n,1);
cvx_begin
variable x(n)
minimize( norm( A*x-b ) )
cvx_end
echo off
n = 100;
A = randn(2*n,n);
b = randn(2*n,1);
cvx_begin
variable x(n)
minimize( norm( A*x-b ) )
cvx_end
Calling sedumi: 201 variables, 101 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 = 101, order n = 3, dim = 202, blocks = 2
nnz(A) = 20001 + 0, nnz(ADA) = 10201, nnz(L) = 5151
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 6.78E+00 0.000
1 : -7.73E+00 1.60E+00 0.000 0.2367 0.9000 0.9000 -0.46 1 1 2.0E+00
2 : -9.75E+00 1.42E-01 0.000 0.0886 0.9900 0.9900 0.99 1 1 2.0E-01
3 : -9.54E+00 5.70E-05 0.219 0.0004 0.9999 0.9999 1.03 1 1 8.3E-05
4 : -9.54E+00 2.62E-07 0.000 0.0046 0.9990 0.9990 1.28 1 1 2.9E-07
5 : -9.54E+00 3.59E-14 0.000 0.0000 1.0000 1.0000 1.00 1 1 4.1E-14
iter seconds digits c*x b*y
5 0.0 Inf -9.5449220247e+00 -9.5449220247e+00
|Ax-b| = 2.5e-14, [Ay-c]_+ = 6.5E-14, |x|= 1.4e+00, |y|= 9.6e+00
Detailed timing (sec)
Pre IPM Post
1.000E-02 4.000E-02 1.000E-02
Max-norms: ||b||=1, ||c|| = 3.229561e+00,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 1.
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Status: Solved
Optimal value (cvx_optval): +9.54492
echo off