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 SDPT3 4.0: 20 variables, 10 equality constraints
For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------
num. of constraints = 10
dim. of linear var = 20
*******************************************************************
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+01|8.5e+00|2.0e+03| 1.224551e+01 0.000000e+00| 0:0:00| chol 1 1
1|0.716|0.990|1.9e+01|1.7e-01|6.1e+02|-7.208277e+00 2.426922e+00| 0:0:00| chol 1 1
2|0.920|1.000|1.5e+00|8.5e-03|4.6e+01|-9.397288e-01 3.491295e+00| 0:0:00| chol 1 1
3|0.413|1.000|8.7e-01|8.5e-04|3.6e+01|-3.808073e-01 5.218247e+01| 0:0:00| chol 1 1
4|0.124|0.458|7.7e-01|5.0e-04|9.8e+01| 1.190177e-01 4.439085e+02| 0:0:00| chol 1 1
5|0.052|0.190|7.3e-01|4.0e-04|5.3e+02|-1.343423e-02 5.384123e+03| 0:0:00| chol 1 1
6|0.064|1.000|6.8e-01|8.5e-07|1.7e+04| 2.845973e-02 7.408387e+05| 0:0:00| chol 1 2
7|0.020|1.000|6.7e-01|2.1e-07|4.2e+06| 2.126749e-02 1.432853e+09| 0:0:00| chol 2 2
8|0.099|1.000|6.3e-01|2.2e-02|1.6e+13| 9.235089e-02 1.631005e+14| 0:0:00| chol 2 2
9|0.083|1.000|5.8e-01|2.6e+00|2.0e+14| 8.554457e-02 1.955677e+16| 0:0:00|
sqlp stop: primal problem is suspected of being infeasible
-------------------------------------------------------------------
number of iterations = 9
residual of primal infeasibility
certificate (y,Z) = 6.89e-16
reldist to infeas. <= 4.72e-17
Total CPU time (secs) = 0.06
CPU time per iteration = 0.01
termination code = 1
DIMACS: 6.9e-01 0.0e+00 4.4e+00 0.0e+00 -1.0e+00 1.0e-02
-------------------------------------------------------------------
------------------------------------------------------------
Status: Unbounded
Optimal value (cvx_optval): -Inf
echo off