Hi, when launch a cvx problem, it returns a 76x76 NaN matrix. In particular, this is the code I launched:
in the “main” script,
[L_recovered,Ck]= laplacian_learning(Y, U_recovered, S_recovered,param, 'TV');
where Y is a 76x400 matrix, U_recovered a 76x76 matrix and S_recovered a 76x400 matrix.
param and ‘TV’ are two parameters needed for the function laplacian_learning, that is the following:
support=[];
trace_constraint=param.trace_constraint;
for i=1:param.N
if norm(S(i,:)) ~=0
support= [support i];
end
end
Uk(:, 1:param.K)= U(:,support); % support first K columns
Sk(1:param.K, :)= S(support,:); % WARNING
switch method
case 'TV'
disp('METHOD: TOTAL VARIATION BASED LEARNING' )
cvx_clear
cvx_begin
variable L_recovered(param.N,param.N) semidefinite % encode the simmetry
variable Ck(param.K,param.K) semidefinite
Objective = sum(sum(repmat(-L_recovered,1,size(Y,2)).* abs(diffmat(Y)))) + param.mu* sum_square(vec(L_recovered))
minimize Objective
subject to
L_recovered*Uk==Uk*Ck
L_recovered*ones(param.N,1)==zeros(param.N,1)
triu(L_recovered,1)<=0; % off diagonal <=0
%diag(L_recovered)>=0; not necesary since semidefinite
trace(L_recovered)==trace_constraint;
cvx_end
The status is INFEASIBLE. In particular this are the message during the resolution cvx process:
Objective =
cvx convex expression (scalar)
Calling SDPT3 4.0: 18575 variables, 5007 equality constraints
For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------
num. of constraints = 5007
dim. of sdp var = 140, num. of sdp blk = 2
dim. of socp var = 5778, num. of socp blk = 1
dim. of linear var = 2850
dim. of free var = 4941 *** convert ublk to lblk
*******************************************************************
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|7.5e+01|1.0e+02|1.0e+13|-1.465070e-02 0.000000e+00| 0:0:09| chol 1 1
1|0.423|0.272|4.3e+01|7.5e+01|2.9e+12| 1.677289e+09 -2.532748e+07| 0:0:16| chol 1 1
2|0.905|0.776|4.1e+00|1.7e+01|5.0e+11| 2.878037e+09 1.651881e+07| 0:0:24| chol 1 1
3|0.873|0.964|5.2e-01|7.3e-01|2.1e+10| 1.724017e+09 -3.392050e+06| 0:0:31| chol 1 1
4|0.905|0.747|4.9e-02|2.3e-01|5.7e+09| 6.088070e+08 -4.120711e+06| 0:0:39| chol 1 1
5|0.336|0.237|3.2e-02|1.8e-01|4.1e+09| 4.530588e+08 -4.165774e+06| 0:0:46| chol 1 1
6|0.379|0.513|2.0e-02|9.8e-02|2.1e+09| 3.734173e+08 -4.311236e+06| 0:0:54| chol 1 1
7|0.687|0.245|6.3e-03|8.0e-02|1.4e+09| 2.603302e+08 -4.314254e+06| 0:1:01| chol 1 1
8|0.491|0.412|3.2e-03|5.0e-02|8.1e+08| 2.062424e+08 -4.333582e+06| 0:1:09| chol 1 1
9|0.931|0.227|2.2e-04|4.0e-02|4.5e+08| 1.149104e+08 -4.332472e+06| 0:1:16| chol 1 1
10|0.794|0.401|4.6e-05|2.4e-02|2.1e+08| 6.378960e+07 -4.339542e+06| 0:1:23| chol 1 1
11|0.296|0.354|3.2e-05|1.6e-02|1.4e+08| 4.678876e+07 -4.355095e+06| 0:1:31| chol 1 1
12|0.460|0.212|1.7e-05|1.2e-02|1.0e+08| 2.302582e+07 -4.364167e+06| 0:1:39| chol 1 1
13|0.491|0.244|8.8e-06|9.5e-03|7.4e+07| 6.629921e+06 -4.371487e+06| 0:1:47| chol 1 1
14|0.396|0.263|5.3e-06|7.0e-03|5.7e+07|-1.715012e+06 -4.366695e+06| 0:1:54| chol 1 1
15|0.388|0.237|3.3e-06|5.3e-03|4.8e+07|-7.962960e+06 -4.374278e+06| 0:2:02| chol 1 1
16|0.176|0.192|2.7e-06|5.7e-03|5.6e+07|-1.070975e+07 -4.432430e+06| 0:2:10| chol 2 2
17|0.037|0.024|2.6e-06|7.5e-03|7.3e+07|-1.077593e+07 -4.617117e+06| 0:2:18| chol 1 2
18|0.231|0.061|2.0e-06|9.3e-03|1.0e+08|-1.225433e+07 -4.750541e+06| 0:2:26| chol 1 2
19|0.293|0.175|1.4e-06|1.0e-02|1.2e+08|-1.377679e+07 -4.997335e+06| 0:2:34| chol 1 2
20|0.222|0.205|1.1e-06|8.1e-03|1.0e+08|-1.464791e+07 -5.238880e+06| 0:2:41| chol 2 2
21|0.325|0.099|7.4e-07|9.8e-03|1.4e+08|-1.664286e+07 -5.343499e+06| 0:2:50| chol 1 2
22|0.524|0.262|3.5e-07|7.2e-03|1.2e+08|-1.968790e+07 -5.603888e+06| 0:2:57| chol 2 2
23|0.259|0.285|2.6e-07|5.2e-03|9.2e+07|-2.243762e+07 -5.792852e+06| 0:3:06| chol 1 2
24|0.162|0.218|2.2e-07|4.0e-03|7.5e+07|-2.538393e+07 -5.906786e+06| 0:3:13| chol 2 2
25|0.489|0.153|1.1e-07|4.7e-03|1.3e+08|-3.781598e+07 -6.118205e+06| 0:3:21| chol 2 2
26|0.709|0.243|3.2e-08|3.5e-03|1.5e+08|-5.784711e+07 -6.202394e+06| 0:3:30| chol 2 2
27|0.437|0.258|1.8e-08|2.6e-03|1.3e+08|-8.610275e+07 -6.387962e+06| 0:3:38| chol 2 2
28|0.390|0.434|1.1e-08|1.5e-03|7.0e+07|-1.503779e+08 -6.531525e+06| 0:3:47| chol 2 2
29|0.057|0.094|1.0e-08|2.0e-03|2.3e+08|-2.451643e+08 -6.582697e+06| 0:3:55| chol 2 2
30|0.398|0.153|6.3e-09|2.4e-03|8.2e+08|-5.769785e+08 -6.619501e+06| 0:4:03| chol 2 2
31|1.000|0.152|2.3e-11|2.9e-03|3.4e+09|-1.735729e+09 -6.613883e+06| 0:4:12| chol 2 2
32|1.000|0.350|7.2e-11|1.9e-03|3.9e+09|-4.096651e+09 -6.596760e+06| 0:4:21| chol 2 2
33|1.000|0.171|4.1e-10|2.3e-03|2.5e+10|-1.870457e+10 -6.635377e+06| 0:4:32| chol 2 2
34|1.000|0.301|5.3e-10|1.6e-03|3.8e+10|-5.812919e+10 -6.684811e+06| 0:4:41| chol 2 2
35|1.000|0.116|1.8e-08|2.1e-03|4.6e+11|-3.910698e+11 -6.733064e+06| 0:4:49| chol 2 2
36|1.000|0.294|1.6e-08|1.5e-03|7.5e+11|-1.361247e+12 -7.703783e+06| 0:4:58|
sqlp stop: dual problem is suspected of being infeasible
-------------------------------------------------------------------
number of iterations = 36
residual of dual infeasibility
certificate X = 4.78e-06
reldist to infeas. <= 6.06e-10
Total CPU time (secs) = 297.60
CPU time per iteration = 8.27
termination code = 2
DIMACS: 3.3e-07 0.0e+00 2.1e-03 0.0e+00 -1.0e+00 5.5e-01
-------------------------------------------------------------------
------------------------------------------------------------
Status: Infeasible
Optimal value (cvx_optval): +Inf
Which could the problem be?