When I ran it, sedumi failed, and sdpt3 succeeded.

Here is the sedumi output

```
Calling SeDuMi 1.34: 6 variables, 3 equality constraints
For improved efficiency, SeDuMi is solving the dual problem.
------------------------------------------------------------
SeDuMi 1.34 (beta) 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 = 3, order n = 7, dim = 7, blocks = 1
nnz(A) = 18 + 0, nnz(ADA) = 9, nnz(L) = 6
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 5.23E+03 0.000
1 : 0.00E+00 1.38E+00 0.000 0.0003 0.9999 0.9999 1.00 1 1 1.0E+00
Run into numerical problems.
iter seconds digits c*x b*y
1 0.0 4.2 5.9977037191e+00 0.0000000000e+00
|Ax-b| = 8.1e-12, [Ay-c]_+ = 8.7E+00, |x|= 2.4e+00, |y|= 4.8e+00
No sensible solution found.
Detailed timing (sec)
Pre IPM Post
7.001E-03 1.700E-02 2.002E-03
Max-norms: ||b||=0, ||c|| = 3.656073e+04,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 5.14829.
------------------------------------------------------------
Status: Failed
Optimal value (cvx_optval): NaN
```

Here is the sdpt3 output:

```
Calling SDPT3 4.0: 6 variables, 3 equality constraints
For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------
num. of constraints = 3
dim. of linear var = 6
*******************************************************************
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||1.1e-05||2.6e+00||3.8e+06|| 6.000004e+01 0.000000e+00|| 0:0:00|| chol 1 1
1||1.000||0.989||4.6e-03||2.9e-02||4.1e+04|| 5.998078e+01 0.000000e+00|| 0:0:00|| chol 1 1
2||1.000||0.991||2.1e-06||2.7e-04||4.5e+02|| 5.982284e+01 0.000000e+00|| 0:0:00|| chol 1 1
3||1.000||1.000||9.8e-07||4.6e-07||4.6e+01|| 4.516516e+01 0.000000e+00|| 0:0:00|| chol 1 1
4||0.990||1.000||9.6e-09||2.0e-07||4.5e-01|| 4.516516e-01 0.000000e+00|| 0:0:00|| chol 1 1
5||0.990||1.000||1.0e-10||2.3e-09||4.8e-03|| 4.752003e-03 0.000000e+00|| 0:0:00|| chol 1 1
6||0.989||1.000||1.1e-12||5.9e-11||5.2e-05|| 5.217583e-05 0.000000e+00|| 0:0:00|| chol 1 1
7||0.989||1.000||1.2e-14||1.0e-12||5.7e-07|| 5.733490e-07 0.000000e+00|| 0:0:01|| chol 1 1
8||1.000||1.000||4.2e-20||1.0e-12||6.3e-09|| 6.300528e-09 0.000000e+00|| 0:0:01||
stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
number of iterations = 8
primal objective value = 6.30052846e-09
dual objective value = 0.00000000e+00
gap := trace(XZ) = 6.30e-09
relative gap = 6.30e-09
actual relative gap = 6.30e-09
rel. primal infeas = 4.25e-20
rel. dual infeas = 1.00e-12
norm(X), norm(y), norm(Z) = 2.6e-09, 4.8e+00, 2.4e+00
norm(A), norm(b), norm(C) = 1.8e+04, 1.0e+00, 6.3e+04
Total CPU time (secs) = 0.50
CPU time per iteration = 0.06
termination code = 0
DIMACS: 4.2e-20 0.0e+00 1.7e-12 0.0e+00 6.3e-09 6.3e-09
-------------------------------------------------------------------
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -6.30053e-09
>> disp(x)
-4.7641
0.4962
-0.2270
-0.4415
```

So how could you get a solution which does not satisfy the constraints? Because it was not a solution, and the solver reported that it failed. The value of x at the point of solver exit is what you saw to be infeasible, and indeed it is infeasible. if the solver claimed to solve the problem and produced an argmin which was not feasible within tolerance, then you would have a reason to complain.

The value of x at the end of the successful sdpt3 run is indeed feasible. The x, which I didn’t show, at the end of the failed sedumi run is infeasible - as I said, the solver admitted to failing, so I am not complaining that upon CVX exit the x is infeasible.