Hi. I’ve been having an issue for a while where the feasibility problem is solved (implying the existence of a solution). However when I take the next step, and attempt to make this a minimization problem rather than a feasibility problem, cvx now fails to converge to a solution. P.S. I’m sorry that the last bit of results are bolded, I’m not familiar with this markup environment and I don’t know how to unbold it.
An analogy would be to say “find x such that x < 10,” and then after that is shown to be feasible, you might introduce a new optimization variable b and say “minimize b such that x < b, and b > 9.” The problem I’m having is that cvx fails to find x in the second case. So I’m wondering if there is something I could be doing differently to make this easier to solve (if it’s a numerical issue).
Any thoughts are appreciated. This could of course be addressed by turning this into a sort of bisection problem, and sequentially determining the feasibility of systems with successively smaller bounds. But my actual research problem is a bit more complicated, and I’m wondering if this issue is indicative of some bigger numerical challenge.
This is my first time posting here, so perhaps I don’t know the correct etiquette when asking questions. But I will provide some more context if anyone can provide some insight. The specific code involves minimizing the infinity-norm of a dynamic linear system; so what I want to ultimately do is maximize some quantity, eta, which represents the inverse of an upper bound of the norm (so bigger eta means smaller norm
The relevant code follows:
In the commented line, I have replaced eta with a hard-set value of 1E-4. When I uncomment this line and instead comment the “maximize (eta)”, we are left with a feasibility problem where the goal is to show that a solution exists such that the norm of the system is upper bounded by 100. That problem is feasible. The code as shown makes it into a maximization problem, where we attempt to maximize eta (and thus minimize the norm), but in this case the solver fails to find a solution. I don’t think this is necessarily a scale issue; the “lmi1” matrix is 39 by 39.
In the case where I still keep eta as a variable, but just comment out “maximize (eta)” the solver now fails because steps are too short consecutively. Which is even more baffling since this is just a feasibility check, and a feasible solution clearly exists (eta = 1E-4).
cvx_begin
variable X(24,24) symmetric
variable Y(6,24)
variable eta(1,1)
lmi1 = -[A*X + X'*A' + B_u*Y + Y'*B_u' + eta*(B_w)*B_w', (C_z*X + D_uz*Y)';
C_z*X + D_uz*Y, -eye(size(C_z, 1));];
% lmi1 = -[AX + X’A’ + B_uY + Y’B_u’ + (1E-4)(B_w)B_w’, (C_zX + D_uzY)’;
% C_zX + D_uzY, -eye(size(C_z, 1));];
maximize (eta)
subject to
X == semidefinite(24);
lmi1 == semidefinite(length(lmi1));
cvx_end
My feasible output is as follows:
Calling SDPT3 4.0: 1188 variables, 552 equality constraints
For improved efficiency, SDPT3 is solving the dual problem.
num. of constraints = 552
dim. of sdp var = 63, num. of sdp blk = 2
dim. of free var = 108 convert ublk to lblk
number of nearly dependent constraints = 39
To remove these constraints, re-run sqlp.m with OPTIONS.rmdepconstr = 1.
SDPT3: Infeasible path-following algorithms
version predcorr gam expon scale_data
HKM 1 0.000 1 0
it pstep dstep pinfeas dinfeas gap prim-obj dual-obj cputime
0|0.000|0.000|3.3e+06|1.0e+01|6.3e+07|-1.203825e+06 0.000000e+00| 0:0:00| spchol 1 1
1|0.286|0.462|2.3e+06|5.4e+00|3.6e+07|-8.567407e+05 0.000000e+00| 0:0:00| chol 1 1
2|0.777|0.957|5.2e+05|2.3e-01|4.3e+06|-1.885866e+05 0.000000e+00| 0:0:00| chol 1 2
3|0.814|0.359|9.7e+04|1.5e-01|1.4e+06|-3.299903e+04 0.000000e+00| 0:0:00| chol 1 1
4|0.903|0.545|9.4e+03|6.8e-02|3.8e+05|-2.518695e+03 0.000000e+00| 0:0:01| chol 1 1
5|0.816|0.552|1.7e+03|3.1e-02|1.5e+05|-1.190875e+02 0.000000e+00| 0:0:01| chol 1 1
6|0.793|0.343|3.6e+02|2.0e-02|9.2e+04| 2.680762e+02 0.000000e+00| 0:0:01| chol 1 1
7|0.836|0.365|5.9e+01|1.3e-02|5.7e+04| 3.374172e+02 0.000000e+00| 0:0:01| chol 1 1
8|0.742|0.367|1.5e+01|8.1e-03|3.6e+04| 3.427661e+02 0.000000e+00| 0:0:01| chol 1 1
9|0.555|0.367|6.7e+00|5.1e-03|2.3e+04| 3.446138e+02 0.000000e+00| 0:0:01| chol 1 1
10|0.611|0.293|2.6e+00|3.6e-03|1.6e+04| 3.380835e+02 0.000000e+00| 0:0:01| chol 1 1
11|0.721|0.451|7.3e-01|2.0e-03|8.5e+03| 3.253958e+02 0.000000e+00| 0:0:01| chol 1 1
12|0.856|0.598|1.1e-01|8.0e-04|3.4e+03| 2.945643e+02 0.000000e+00| 0:0:01| chol 1 1
13|0.778|0.443|2.3e-02|4.4e-04|1.7e+03| 2.373356e+02 0.000000e+00| 0:0:01| chol 1 1
14|0.267|0.094|1.7e-02|4.0e-04|1.7e+03| 2.134356e+02 0.000000e+00| 0:0:02| chol 1 1
15|0.296|0.292|1.2e-02|2.9e-04|1.3e+03| 1.885676e+02 0.000000e+00| 0:0:02| chol 1 1
16|0.368|0.133|7.7e-03|2.5e-04|1.1e+03| 1.558719e+02 0.000000e+00| 0:0:02| chol 1 1
17|0.403|0.325|4.6e-03|1.7e-04|8.1e+02| 1.245146e+02 0.000000e+00| 0:0:02| chol 1 2
18|0.424|0.153|2.6e-03|1.4e-04|7.0e+02| 9.432021e+01 0.000000e+00| 0:0:02| chol 1 1
19|0.464|0.363|1.4e-03|9.1e-05|4.7e+02| 6.869055e+01 0.000000e+00| 0:0:02| chol 1 1
20|0.445|0.156|7.8e-04|7.7e-05|4.1e+02| 5.008803e+01 0.000000e+00| 0:0:02| chol 1 2
21|0.325|0.135|5.3e-04|6.7e-05|3.8e+02| 4.164956e+01 0.000000e+00| 0:0:02| chol 1 2
22|0.316|0.126|3.6e-04|5.9e-05|3.6e+02| 3.565234e+01 0.000000e+00| 0:0:02| chol 2 2
23|0.316|0.126|2.5e-04|5.2e-05|3.4e+02| 3.125998e+01 0.000000e+00| 0:0:02| chol 2 2
24|0.321|0.129|1.7e-04|4.5e-05|3.2e+02| 2.798128e+01 0.000000e+00| 0:0:02| chol 2 2
25|0.329|0.133|1.1e-04|3.9e-05|3.0e+02| 2.549477e+01 0.000000e+00| 0:0:03| chol 2 2
26|0.332|0.135|7.6e-05|3.4e-05|2.9e+02| 2.369316e+01 0.000000e+00| 0:0:03| chol 2 2
27|0.343|0.140|5.0e-05|3.0e-05|2.7e+02| 2.227170e+01 0.000000e+00| 0:0:03| chol 2 2
28|0.354|0.148|3.3e-05|2.5e-05|2.5e+02| 2.102256e+01 0.000000e+00| 0:0:03| chol 2 2
29|0.381|0.157|2.2e-05|2.2e-05|2.3e+02| 1.973887e+01 0.000000e+00| 0:0:03| chol 2 2
30|0.392|0.170|1.5e-05|1.8e-05|2.1e+02| 1.838613e+01 0.000000e+00| 0:0:03| chol 2 2
31|0.472|0.200|1.1e-05|1.5e-05|1.8e+02| 1.615069e+01 0.000000e+00| 0:0:03| chol 2 2
32|0.549|0.258|7.1e-06|1.1e-05|1.5e+02| 1.304557e+01 0.000000e+00| 0:0:03| chol 2 3
33|0.706|0.333|4.2e-06|7.5e-06|1.0e+02| 9.115838e+00 0.000000e+00| 0:0:03| chol 2 2
34|0.909|0.625|1.0e-06|2.8e-06|4.0e+01| 5.029560e+00 0.000000e+00| 0:0:03| chol 2 3
35|1.000|0.177|1.5e-06|2.4e-06|3.0e+01| 3.323169e+00 0.000000e+00| 0:0:03| chol 2 3
36|1.000|0.280|1.5e-06|1.8e-06|2.2e+01| 2.409180e+00 0.000000e+00| 0:0:03| chol 2 3
37|1.000|0.297|1.5e-06|1.3e-06|1.5e+01| 1.753830e+00 0.000000e+00| 0:0:04| chol 2 4
38|1.000|0.317|1.2e-06|9.0e-07|1.1e+01| 1.290304e+00 0.000000e+00| 0:0:04| chol 3 3
39|1.000|0.396|7.6e-07|5.6e-07|6.5e+00| 8.393190e-01 0.000000e+00| 0:0:04| chol 3 4
40|1.000|0.441|3.7e-07|3.3e-07|3.6e+00| 5.183363e-01 0.000000e+00| 0:0:04| chol 4 4
41|1.000|0.487|1.4e-07|1.8e-07|1.7e+00| 3.216155e-01 0.000000e+00| 0:0:04| chol 5 5
42|1.000|0.433|6.8e-08|1.1e-07|8.8e-01| 2.098654e-01 0.000000e+00| 0:0:04| chol 6 5
43|1.000|0.511|2.5e-08|5.7e-08|3.6e-01| 1.196956e-01 0.000000e+00| 0:0:04| chol 7 8
44|1.000|0.496|9.4e-09|3.2e-08|1.2e-01| 5.376328e-02 0.000000e+00| 0:0:04| chol 6 7
45|1.000|0.648|2.0e-09|1.3e-08|2.6e-02| 1.620949e-02 0.000000e+00| 0:0:04| chol 8 16
46|1.000|0.470|8.7e-10|1.4e-08|4.4e-03| 2.456181e-03 0.000000e+00| 0:0:05| chol 24 14
47|1.000|0.684|2.8e-10|3.0e-09|4.4e-04| 3.147500e-04 0.000000e+00| 0:0:05| chol
linsysolve: Schur complement matrix not positive definite
switch to LU factor. lu 30 ^ 6
48|0.762|0.776|1.4e-10|5.3e-10|1.0e-04| 8.556438e-05 0.000000e+00| 0:0:05| lu 30 ^12
49|0.957|0.790|1.3e-11|1.6e-10|6.0e-06| 4.810886e-06 0.000000e+00| 0:0:05| lu 11 ^20
50|0.264|0.307|3.7e-11|9.6e-11|4.2e-06| 3.699605e-06 0.000000e+00| 0:0:05| lu 30 ^ 9
51|0.733|0.917|1.4e-11|9.9e-11|1.2e-06| 1.046132e-06 0.000000e+00| 0:0:05| lu 11 30
52|0.156|0.127|2.0e-11|9.3e-11|9.9e-07| 9.030236e-07 0.000000e+00| 0:0:06| lu 30 ^ 7
53|0.252|0.941|1.6e-11|8.0e-11|7.5e-07| 6.704352e-07 0.000000e+00| 0:0:06| lu 13 ^28
54|0.303|0.490|1.5e-11|7.6e-11|5.2e-07| 4.695927e-07 0.000000e+00| 0:0:06| lu 30 ^11
55|0.041|0.147|1.4e-11|7.9e-11|4.9e-07| 4.547121e-07 0.000000e+00| 0:0:06| lu 30 ^25
56|0.023|0.053|1.4e-11|5.9e-11|4.8e-07| 4.476404e-07 0.000000e+00| 0:0:06|
stop: steps too short consecutively
number of iterations = 56
primal objective value = 4.47640419e-07
dual objective value = 0.00000000e+00
gap := trace(XZ) = 4.77e-07
relative gap = 4.77e-07
actual relative gap = 4.48e-07
rel. primal infeas (scaled problem) = 1.44e-11
rel. dual " " " = 5.94e-11
rel. primal infeas (unscaled problem) = 0.00e+00
rel. dual " " " = 0.00e+00
norm(X), norm(y), norm(Z) = 1.3e-03, 2.0e+06, 2.9e+10
norm(A), norm(b), norm© = 6.6e+05, 1.0e+00, 5.3e+04
Total CPU time (secs) = 6.34
CPU time per iteration = 0.11
termination code = -5
DIMACS: 1.4e-11 0.0e+00 2.0e-10 0.0e+00 4.5e-07 4.8e-07
Status: Inaccurate/Solved
Optimal value (cvx_optval): -4.4764e-07
while my “failed” output (max iterations is reached, but clearly this solution does not seem like it’s going anywhere) is
Calling SDPT3 4.0: 1189 variables, 553 equality constraints
For improved efficiency, SDPT3 is solving the dual problem.
num. of constraints = 553
dim. of sdp var = 63, num. of sdp blk = 2
dim. of linear var = 1
dim. of free var = 108 convert ublk to lblk
number of nearly dependent constraints = 39
To remove these constraints, re-run sqlp.m with OPTIONS.rmdepconstr = 1.
SDPT3: Infeasible path-following algorithms
version predcorr gam expon scale_data
HKM 1 0.000 1 0
it pstep dstep pinfeas dinfeas gap prim-obj dual-obj cputime
0|0.000|0.000|6.0e+09|6.8e+08|3.3e+11| 2.423149e+02 0.000000e+00| 0:0:00| spchol 1 2
1|0.000|0.003|6.0e+09|6.7e+08|3.7e+11| 2.423150e+02 1.659480e+01| 0:0:00| chol 2 2
2|0.005|0.000|6.0e+09|6.7e+08|3.7e+11| 2.424527e+02 2.057097e+01| 0:0:00| chol 2 2
3|0.005|0.002|6.0e+09|6.7e+08|3.7e+11| 2.426283e+02 3.719155e+01| 0:0:01| chol 2 2
4|0.009|0.003|5.9e+09|6.7e+08|3.7e+11| 2.428799e+02 5.987569e+01| 0:0:01| chol 2 2
5|0.019|0.005|5.8e+09|6.7e+08|3.7e+11| 2.433303e+02 9.496288e+01| 0:0:01| chol 2 2
6|0.025|0.009|5.6e+09|6.6e+08|3.6e+11| 2.438916e+02 1.552193e+02| 0:0:01| chol 2 2
7|0.055|0.012|5.3e+09|6.5e+08|3.5e+11| 2.450676e+02 2.367309e+02| 0:0:01| chol 2 2
8|0.059|0.026|5.0e+09|6.4e+08|3.4e+11| 2.462430e+02 4.001487e+02| 0:0:01| chol 2 2
9|0.142|0.031|4.3e+09|6.2e+08|3.2e+11| 2.488394e+02 5.864318e+02| 0:0:01| chol 2 2
10|0.144|0.069|3.7e+09|5.7e+08|3.0e+11| 2.510827e+02 9.888177e+02| 0:0:01| chol 2 2
11|0.306|0.077|2.6e+09|5.3e+08|2.6e+11| 2.552522e+02 1.415330e+03| 0:0:01| chol 2 2
12|0.301|0.158|1.8e+09|4.5e+08|2.1e+11| 2.583137e+02 2.282197e+03| 0:0:01| chol 2 2
13|0.500|0.165|8.9e+08|3.7e+08|1.7e+11| 2.624732e+02 3.169173e+03| 0:0:01| chol 2 2
14|0.260|0.208|6.6e+08|2.9e+08|1.3e+11| 2.646442e+02 4.822779e+03| 0:0:02| chol 2 2
15|0.472|0.152|3.5e+08|2.5e+08|1.1e+11| 2.689140e+02 5.989161e+03| 0:0:02| chol 2 2
16|0.464|0.183|1.9e+08|2.0e+08|8.5e+10| 2.742777e+02 8.203634e+03| 0:0:02| chol 2 2
17|0.560|0.190|8.2e+07|1.7e+08|6.7e+10| 2.820396e+02 1.165743e+04| 0:0:02| chol 2 3
18|0.500|0.224|4.1e+07|1.3e+08|5.1e+10| 2.897046e+02 1.856580e+04| 0:0:02| chol 3 3
19|0.592|0.239|1.7e+07|9.8e+07|3.8e+10| 2.966113e+02 2.802781e+04| 0:0:02| chol 3 3
20|0.602|0.190|6.7e+06|7.9e+07|3.1e+10| 3.073468e+02 4.497793e+04| 0:0:02| chol 3 3
21|0.384|0.271|4.1e+06|5.8e+07|2.3e+10| 3.118560e+02 8.065350e+04| 0:0:02| chol 3 3
22|0.594|0.189|1.7e+06|4.7e+07|1.8e+10| 3.191279e+02 1.069797e+05| 0:0:02| chol 3 3
23|0.428|0.218|9.6e+05|3.7e+07|1.4e+10| 3.246658e+02 1.588358e+05| 0:0:02| chol 3 3
24|0.676|0.200|3.1e+05|2.9e+07|1.1e+10| 3.319454e+02 2.044433e+05| 0:0:02| chol 4 4
25|0.515|0.252|1.5e+05|2.2e+07|8.6e+09| 3.370143e+02 2.850127e+05| 0:0:03| chol 4 4
26|0.721|0.243|4.2e+04|1.7e+07|6.5e+09| 3.430621e+02 3.318820e+05| 0:0:03| chol 4 5
27|0.525|0.234|2.0e+04|1.3e+07|5.0e+09| 3.477637e+02 4.028679e+05| 0:0:03| chol 5 7
28|0.680|0.370|6.4e+03|8.0e+06|3.2e+09| 3.512639e+02 3.418697e+05| 0:0:03| chol 8 7
29|0.429|0.204|3.7e+03|6.4e+06|2.5e+09| 3.543498e+02 3.250129e+05| 0:0:03| chol 9 9
30|0.622|0.334|1.4e+03|4.2e+06|1.7e+09| 3.566896e+02 2.466601e+05| 0:0:03| chol 7 9
31|0.823|0.550|2.4e+02|1.9e+06|7.6e+08| 3.578368e+02 1.194213e+05| 0:0:03| chol 8 9
32|0.244|0.068|1.8e+02|1.8e+06|7.2e+08| 3.594876e+02 1.124025e+05| 0:0:03| chol 16 30
33|0.170|0.109|1.5e+02|1.6e+06|6.4e+08| 3.614413e+02 1.030113e+05| 0:0:03| chol 10 15
34|0.255|0.111|1.1e+02|1.4e+06|5.8e+08| 3.648751e+02 9.709624e+04| 0:0:04| chol 27 22
35|0.319|0.155|7.8e+01|1.2e+06|5.0e+08| 3.693212e+02 9.016650e+04| 0:0:04| chol 26 30
36|0.548|0.314|3.5e+01|8.2e+05|3.4e+08| 3.731507e+02 6.801166e+04| 0:0:04| chol 23 17
37|0.742|0.421|9.1e+00|4.7e+05|2.0e+08| 3.755223e+02 4.058459e+04| 0:0:04| chol 26 30
38|0.191|0.054|7.3e+00|4.5e+05|1.9e+08| 3.792542e+02 3.694062e+04| 0:0:04| chol
warning: symqmr failed: 0.3
switch to LU factor. lu 16 ^12
39|0.047|0.075|7.0e+00|4.1e+05|1.8e+08| 3.828099e+02 2.906123e+04| 0:0:05| lu 23 4
40|0.242|0.075|5.3e+00|3.8e+05|1.7e+08| 3.898972e+02 2.652113e+04| 0:0:05| lu 11 ^11
41|0.015|0.026|5.2e+00|3.7e+05|1.6e+08| 3.913053e+02 2.619236e+04| 0:0:05| lu 30 3
42|0.199|0.177|4.2e+00|3.1e+05|1.4e+08| 3.964083e+02 2.276090e+04| 0:0:05| lu 29 2
43|0.416|0.137|2.4e+00|2.6e+05|1.2e+08| 4.044833e+02 2.031385e+04| 0:0:05| lu 11 ^ 6
44|0.136|0.072|2.1e+00|2.4e+05|1.2e+08| 4.197357e+02 1.915583e+04| 0:0:05| lu 24 9
45|0.391|0.150|1.3e+00|2.1e+05|1.0e+08| 4.327931e+02 1.714880e+04| 0:0:06| lu 29 ^ 9
46|0.101|0.153|1.2e+00|1.8e+05|8.8e+07| 4.380963e+02 1.548094e+04| 0:0:06| lu 30 4
47|0.913|0.438|1.0e-01|9.9e+04|4.9e+07| 4.415107e+02 8.961268e+03| 0:0:06| lu 30 ^ 7
48|0.770|0.493|2.3e-02|5.0e+04|2.5e+07| 4.437505e+02 4.611701e+03| 0:0:06| lu 26 3
49|0.545|0.250|1.0e-02|3.8e+04|1.9e+07| 4.464402e+02 3.490966e+03| 0:0:06| lu 16 2
50|0.461|0.204|5.7e-03|3.0e+04|1.5e+07| 4.491277e+02 2.799732e+03| 0:0:06| lu 14 9
51|0.085|0.037|5.2e-03|2.9e+04|1.4e+07| 4.518062e+02 2.714234e+03| 0:0:06| lu 30 ^20
52|0.282|0.091|3.7e-03|2.6e+04|1.4e+07| 4.595576e+02 2.499970e+03| 0:0:07| lu 30 7
53|0.480|0.338|1.9e-03|1.7e+04|9.1e+06| 4.666230e+02 1.711938e+03| 0:0:07| lu 30 ^14
54|0.301|0.290|1.3e-03|1.2e+04|6.4e+06| 4.697803e+02 1.234262e+03| 0:0:07| lu 19 30
55|0.067|0.054|1.3e-03|1.2e+04|6.1e+06| 4.721202e+02 1.177245e+03| 0:0:07| lu 16 ^20
56|0.004|0.027|1.2e-03|1.1e+04|5.9e+06| 4.726883e+02 1.157589e+03| 0:0:07| lu 15 ^16
57|0.049|0.025|1.2e-03|1.1e+04|5.8e+06| 4.739063e+02 1.135323e+03| 0:0:08| lu 30 ^11
58|0.003|0.007|1.2e-03|1.1e+04|5.7e+06| 4.744258e+02 1.127028e+03| 0:0:08| lu 29 ^ 4
59|0.053|0.015|1.1e-03|1.1e+04|5.7e+06| 4.791484e+02 1.116769e+03| 0:0:08| lu 30 ^25
60|0.077|0.055|1.0e-03|1.0e+04|5.5e+06| 4.821503e+02 1.066436e+03| 0:0:08| lu 20 ^13
61|0.181|0.060|8.4e-04|9.6e+03|5.3e+06| 4.881858e+02 1.013101e+03| 0:0:08| lu 14 ^26
62|0.085|0.047|7.7e-04|9.2e+03|5.1e+06| 4.995017e+02 9.603902e+02| 0:0:08| lu 12 ^27
63|0.223|0.080|6.0e-04|8.4e+03|4.9e+06| 5.121407e+02 8.995951e+02| 0:0:09| lu 29 ^26
64|0.169|0.140|5.0e-04|7.2e+03|4.3e+06| 5.185124e+02 7.931493e+02| 0:0:09| lu 23 ^17
65|0.264|0.164|3.7e-04|6.1e+03|3.6e+06| 5.252965e+02 6.765466e+02| 0:0:09| lu 12 ^15
66|0.001|0.000|3.8e-04|6.1e+03|3.5e+06| 5.224010e+02 6.764318e+02| 0:0:09| lu 13 ^27
67|0.213|0.031|3.0e-04|5.9e+03|3.5e+06| 5.303777e+02 6.585829e+02| 0:0:09| lu 13 30
68|0.025|0.044|2.9e-04|5.6e+03|3.4e+06| 5.345164e+02 6.253092e+02| 0:0:10| lu 30 ^19
69|0.653|0.064|1.1e-04|5.3e+03|3.3e+06| 5.529126e+02 5.888591e+02| 0:0:10| lu 18 ^21
70|0.052|0.194|1.0e-04|4.2e+03|2.6e+06| 5.539418e+02 4.806528e+02| 0:0:10| lu 30 ^13
71|0.362|0.657|6.6e-05|1.5e+03|9.2e+05| 5.618554e+02 1.832996e+02| 0:0:10| lu 30 ^ 9
72|0.436|0.110|4.2e-05|1.3e+03|8.5e+05| 5.761440e+02 1.630264e+02| 0:0:10| lu 30 ^17
73|1.000|0.220|1.8e-05|1.0e+03|7.1e+05| 6.143265e+02 1.269609e+02| 0:0:11| lu 13 ^ 7
74|0.182|0.302|2.6e-05|7.0e+02|4.9e+05| 6.207686e+02 9.130247e+01| 0:0:11| lu 20 ^17
75|0.521|0.077|3.1e-05|6.5e+02|5.0e+05| 6.639450e+02 8.445973e+01| 0:0:11| lu 30 ^21
76|0.431|0.397|2.3e-05|3.9e+02|3.0e+05| 6.886484e+02 5.004532e+01| 0:0:11| lu 30 ^10
77|0.129|0.126|4.2e-05|3.4e+02|2.7e+05| 7.083385e+02 4.388693e+01| 0:0:11| lu 16 ^ 9
78|0.306|0.113|1.5e-04|3.0e+02|2.7e+05| 7.952529e+02 3.754628e+01| 0:0:11| lu 15 ^18
79|0.208|0.171|1.3e-04|2.5e+02|2.3e+05| 8.498406e+02 3.157560e+01| 0:0:12| lu 30 ^ 9
80|0.754|0.211|8.3e-05|2.0e+02|2.1e+05| 1.080097e+03 2.559976e+01| 0:0:12| lu 11 ^21
81|0.007|0.012|9.3e-05|2.0e+02|2.0e+05| 1.095066e+03 2.489633e+01| 0:0:12| lu 11 30
82|0.014|0.018|1.1e-04|1.9e+02|2.0e+05| 1.087018e+03 2.422377e+01| 0:0:12| lu 30 30
83|0.011|0.016|1.1e-04|1.9e+02|1.9e+05| 1.090931e+03 2.368975e+01| 0:0:12| lu 24 ^ 7
84|0.186|0.068|9.1e-05|1.8e+02|1.9e+05| 1.107635e+03 2.224791e+01| 0:0:12| lu 30 ^23
85|0.140|0.080|8.5e-05|1.6e+02|1.9e+05| 1.225802e+03 1.967137e+01| 0:0:13| lu 11 ^26
86|0.029|0.018|1.8e-04|1.6e+02|1.9e+05| 1.333295e+03 1.902119e+01| 0:0:13| lu 22 3
87|0.067|0.051|1.7e-04|1.5e+02|1.9e+05| 1.372725e+03 1.817243e+01| 0:0:13| lu 16 ^27
88|0.103|0.037|2.1e-04|1.5e+02|1.9e+05| 1.498051e+03 1.752079e+01| 0:0:13| lu 13 5
89|0.077|0.057|2.0e-04|1.4e+02|1.9e+05| 1.559574e+03 1.670763e+01| 0:0:13| lu 12 17
90|0.028|0.052|1.9e-04|1.3e+02|1.8e+05| 1.622699e+03 1.511166e+01| 0:0:13| lu 15 ^ 2
91|0.080|0.019|1.8e-04|1.3e+02|2.0e+05| 1.943100e+03 1.465045e+01| 0:0:13| lu 30 30
92|0.001|0.005|1.8e-04|1.3e+02|2.0e+05| 1.949925e+03 1.453110e+01| 0:0:14| lu 6 2
93|0.196|0.012|5.5e-04|1.3e+02|2.5e+05| 2.987855e+03 1.423957e+01| 0:0:14| lu 25 7
94|0.018|0.020|5.4e-04|1.2e+02|2.3e+05| 5.010329e+03 8.073147e+00| 0:0:14| lu 14 4
95|0.002|0.004|8.3e-04|1.2e+02|2.4e+05| 3.915040e+03 1.069076e+01| 0:0:14| lu 6 2
96|0.027|0.015|9.1e-04|1.2e+02|2.5e+05| 3.131346e+03 1.113281e+01| 0:0:14| lu 8 3
97|0.140|0.015|9.4e-04|1.2e+02|3.3e+05| 6.390254e+03 1.069399e+01| 0:0:14| lu 20 30
98|0.000|0.000|9.6e-04|1.2e+02|3.2e+05| 6.578451e+03 1.038703e+01| 0:0:15| lu 5 2
99|0.016|0.013|9.2e-04|1.2e+02|3.4e+05| 7.445174e+03 1.001145e+01| 0:0:15| lu 6 3
100|0.003|0.002|9.2e-04|1.2e+02|3.5e+05| 5.617423e+03 1.141895e+01| 0:0:15|
sqlp stop: maximum number of iterations reached
-------------------------------------------------------------------
number of iterations = 100
primal objective value = 5.61742255e+03
dual objective value = 1.14189522e+01
gap := trace(XZ) = 3.46e+05
relative gap = 6.14e+01
actual relative gap = 9.96e-01
rel. primal infeas (scaled problem) = 9.22e-04
rel. dual " " " = 1.18e+02
rel. primal infeas (unscaled problem) = 0.00e+00
rel. dual " " " = 0.00e+00
norm(X), norm(y), norm(Z) = 4.3e+04, 4.7e+11, 3.0e+16
norm(A), norm(b), norm(C) = 5.3e+08, 2.0e+00, 4.9e+00
Total CPU time (secs) = 14.88
CPU time per iteration = 0.15
termination code = -6
DIMACS: 9.2e-04 0.0e+00 2.9e+02 0.0e+00 1.0e+00 6.1e+01
Status: Failed
Optimal value (cvx_optval): NaN