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 SDPT3 4.0: 201 variables, 101 equality constraints
For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------
num. of constraints = 101
dim. of socp var = 201, num. of socp blk = 1
*******************************************************************
SDPT3: Infeasible path-following algorithms
*******************************************************************
version predcorr gam expon scale_data
NT 1 0.000 1 0
it pstep dstep pinfeas dinfeas gap prim-obj dual-obj cputime
-------------------------------------------------------------------
0|0.000|0.000|6.6e+00|1.4e+00|2.5e+02| 0.000000e+00 0.000000e+00| 0:0:00| chol 1 1
1|0.941|1.000|3.9e-01|6.3e-03|2.6e+01|-1.275650e+01 -2.180124e+01| 0:0:00| chol 1 1
2|1.000|1.000|7.7e-08|6.3e-04|2.1e+00|-1.004066e+01 -1.215678e+01| 0:0:00| chol 1 1
3|0.987|0.985|1.9e-08|7.1e-05|3.0e-02|-1.087762e+01 -1.090664e+01| 0:0:00| chol 1 1
4|0.989|0.989|6.0e-09|7.0e-06|3.3e-04|-1.088953e+01 -1.088975e+01| 0:0:00| chol 1 1
5|0.989|0.989|6.5e-11|7.8e-08|3.7e-06|-1.088966e+01 -1.088966e+01| 0:0:00| chol 1 1
6|0.989|0.989|7.2e-13|8.7e-10|4.1e-08|-1.088966e+01 -1.088966e+01| 0:0:00|
stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
number of iterations = 6
primal objective value = -1.08896629e+01
dual objective value = -1.08896629e+01
gap := trace(XZ) = 4.07e-08
relative gap = 1.79e-09
actual relative gap = 1.18e-09
rel. primal infeas (scaled problem) = 7.18e-13
rel. dual " " " = 8.70e-10
rel. primal infeas (unscaled problem) = 0.00e+00
rel. dual " " " = 0.00e+00
norm(X), norm(y), norm(Z) = 1.4e+00, 1.1e+01, 1.5e+01
norm(A), norm(b), norm(C) = 1.4e+02, 2.0e+00, 1.6e+01
Total CPU time (secs) = 0.11
CPU time per iteration = 0.02
termination code = 0
DIMACS: 7.2e-13 0.0e+00 3.3e-09 0.0e+00 1.2e-09 1.8e-09
-------------------------------------------------------------------
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +10.8897
echo off