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
Calling SDPT3: 201 variables, 101 equality constraints
For improved efficiency, SDPT3 is solving the dual problem.
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num. of constraints = 101
dim. of socp var = 201, num. of socp blk = 1
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SDPT3: Infeasible path-following algorithms
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version predcorr gam expon scale_data
NT 1 0.000 1 0
it pstep dstep pinfeas dinfeas gap mean(obj) cputime
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0|0.000|0.000|6.6e+00|1.5e+00|2.5e+02| 0.000000e+00| 0:0:00| chol 1 1
1|0.953|1.000|3.1e-01|6.8e-03|2.3e+01|-1.537672e+01| 0:0:00| chol 1 1
2|1.000|1.000|7.4e-08|6.8e-04|1.6e+00|-9.722419e+00| 0:0:00| chol 1 1
3|0.986|0.986|1.8e-08|7.7e-05|2.3e-02|-9.733358e+00| 0:0:00| chol 1 1
4|0.989|0.989|5.8e-09|7.5e-06|2.5e-04|-9.733961e+00| 0:0:00| chol 1 1
5|0.989|0.989|6.3e-11|8.4e-08|2.8e-06|-9.734018e+00| 0:0:00| chol 1 1
6|0.989|0.989|8.0e-13|9.3e-10|3.1e-08|-9.734018e+00| 0:0:01|
stop: max(relative gap, infeasibilities) < 1.49e-08
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number of iterations = 6
primal objective value = -9.73401819e+00
dual objective value = -9.73401821e+00
gap := trace(XZ) = 3.10e-08
relative gap = 1.51e-09
actual relative gap = 8.42e-10
rel. primal infeas = 8.03e-13
rel. dual infeas = 9.32e-10
norm(X), norm(y), norm(Z) = 1.4e+00, 9.8e+00, 1.4e+01
norm(A), norm(b), norm(C) = 1.4e+02, 2.0e+00, 1.5e+01
Total CPU time (secs) = 0.6
CPU time per iteration = 0.1
termination code = 0
DIMACS: 8.0e-13 0.0e+00 4.0e-09 0.0e+00 8.4e-10 1.5e-09
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Status: Solved
Optimal value (cvx_optval): +9.73402