Hi,
I am attempting to solve an SDP problem using CVX. Unfortunately, I haven’t been able to obtain a result, as the solver terminates with the message ‘Status: Infeasible’. The code I am using, and the associated variables are as follows:
cvx_begin sdp
variable gamma_i(N)
minimize(sum(((gamma_i - max_beta)./(min_beta - max_beta))))
subject to
(D - eps.*identity_mat)*diag(gamma_i) - A >= 0;
gamma_i >= min_gamma;
gamma_i <= max_gamma;
cvx_end
N --> 500
max_beta --> 0.0056
min_beta —> 0.0011
D —> diag(delta_i) [500 x 500], where delta_i is a 500x1 vector with all entries being equal to 0.1
eps --> 0.5
min_gamma —> 1/max_beta = 178.2332
max_gamma --> 1/min_beta = 891.1659
A —> 500 x 500 matrix, with dominant eigenvalue 21.38
This code is based on the work completed in this paper:
https://arxiv.org/pdf/1303.3984.pdf (Optimal Vaccine Allocation to Control Epidemic
Outbreaks in Arbitrary Networks)
Log output from the solver would be helpful.
Hi Michal,
Thank you so much for the response!
Here’s the solver log output:
Calling SDPT3 4.0: 126250 variables, 500 equality constraints
For improved efficiency, SDPT3 is solving the dual problem.
num. of constraints = 500
dim. of sdp var = 500, num. of sdp blk = 1
dim. of linear var = 1000
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|3.1e+03|3.1e+01|7.9e+08|-1.469531e+06 0.000000e+00| 0:0:00| spchol 1 1
1|1.000|0.816|9.6e-04|5.7e+00|1.1e+08| 4.013989e+06 1.741893e+03| 0:0:00| chol 1 1
2|1.000|0.910|7.9e-04|5.1e-01|1.1e+07| 2.248266e+06 1.528083e+02| 0:0:00| chol 1 1
3|1.000|0.202|1.7e-04|4.1e-01|1.2e+07|-1.764399e+07 1.262098e+02| 0:0:00| chol 1 1
4|1.000|0.070|2.4e-04|3.8e-01|7.4e+07|-4.142158e+08 1.293318e+02| 0:0:01| chol 1 1
5|0.064|0.017|2.4e-04|3.7e-01|3.4e+08|-5.429773e+09 1.333419e+02| 0:0:01| chol 1 1
6|0.033|0.035|2.4e-04|3.6e-01|1.4e+09|-6.789565e+10 1.303868e+02| 0:0:01| chol 1 1
7|0.002|0.008|2.3e-04|3.6e-01|4.6e+09|-4.299894e+11 1.295038e+02| 0:0:01| chol 1 1
8|0.001|0.005|2.3e-04|3.6e-01|1.7e+10|-3.008545e+12 1.289529e+02| 0:0:01| chol 2 2
9|0.000|0.003|2.3e-04|3.6e-01|6.2e+10|-2.292797e+13 1.286149e+02| 0:0:01| chol 2 2
10|0.000|0.002|2.3e-04|3.5e-01|2.2e+11|-1.875385e+14 1.284368e+02| 0:0:02| chol 2 2
11|0.000|0.001|2.5e-04|3.5e-01|7.5e+11|-1.610789e+15 1.283544e+02| 0:0:02| chol 2 2
12|0.000|0.000|6.8e-04|3.5e-01|2.4e+12|-1.421452e+16 1.283211e+02| 0:0:02| chol 2 2
13|0.000|0.000|5.3e-03|3.5e-01|7.6e+12|-1.269780e+17 1.283089e+02| 0:0:02| chol 2 2
14|0.000|0.000|4.7e-02|3.5e-01|2.3e+13|-1.139688e+18 1.283049e+02| 0:0:02| chol 2 2
15|0.000|0.000|4.9e-02|3.5e-01|8.3e+12|-1.190890e+18 1.283037e+02| 0:0:02| chol 2 2
16|0.000|0.000|5.3e-02|3.5e-01|5.5e+12|-1.286176e+18 1.283034e+02| 0:0:02| chol 2
stop: steps in predictor too short: pstep = 8.79e-07, dstep = 3.83e-06
17|0.000|0.000|5.3e-02|3.5e-01|5.5e+12|-1.286176e+18 1.283034e+02| 0:0:02|
prim_inf,dual_inf,relgap = 5.34e-02, 3.54e-01, 4.26e-06
sqlp stop: dual problem is suspected of being infeasible
number of iterations = 17
residual of dual infeasibility
certificate X = 5.17e-20
reldist to infeas. <= 1.45e-19
Total CPU time (secs) = 2.49
CPU time per iteration = 0.15
termination code = 2
DIMACS: 5.5e-02 0.0e+00 7.9e+00 0.0e+00 -1.0e+00 4.3e-06
Status: Infeasible
Optimal value (cvx_optval): +Inf
Thanks!
You had attempted to solve using only SDP3 solver… It will be appreciative if you share results for Solver Sedumi for comparison
Supra
