Is 'Numerical Problems' is critical error?

[Hamid]

Hi everyone...

When i write my code and use sedumi solver, i face  with 'Numerical Problems' error.

My question is:

Is 'Numerical Problems' is critical error? or Can i ignore this error and use obtained result?  

[Johan Löfberg]

It just emphasis the fact that you always should look at the diagnostic display printed by the solver (look in the solver manual to learn what it says) and that you, as always, have to look at the solution and interpret the solution from your practical needs. Is it sufficiently (close to being) feasible? Are the computed decision variables reasonable? Are the numbers in general reasonable (e.g., if you are computing a feedback law, and the feedback has numbers in the order of 10^10 or some crap like that, the reason sedumi has struggled is precisely due to this and your problem is ill-posed. A feedback law with elements of that size is not something you would like to implement in practice, and it indicates that you should reformulate or at least rescale the model).

Additionally, it is also good practice to always test your model with multiple solvers. Some might have numerical problems (or at least be honest and explicitly tell the user about this) and some may not. If the solutions somewhat agrees, you can typically be more confident, but if they disagree a lot (not accounting for non-unique optimal solutions), you most likely have a problem.

[Hamid]

Thanks Johan.

But i don't know what means  the diagnostic display printed by the solver after running my code?

[Johan Löfberg]

this

>> x = sdpvar(1);solvesdp(x>=0,[],sdpsettings('solver','sedumi'))
 
SeDuMi had unexplained problems, maybe due to linear dependence?
YALMIP tweaks the problem (adds 1e6 magnitude bounds on all variables) and restarts...
 
SeDuMi 1.3 by AdvOL, 2005-2008 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, theta = 0.250, beta = 0.500
eqs m = 1, order n = 4, dim = 4, blocks = 1
nnz(A) = 3 + 0, nnz(ADA) = 1, nnz(L) = 1
 it :     b*y       gap    delta  rate   t/tP*  t/tD*   feas cg cg  prec
  0 :            2.25E+06 0.000
  1 :   0.00E+00 4.28E+05 0.000 0.1900 0.9000 0.9000   1.00  1  0  1.7E+00
  2 :   0.00E+00 2.06E+03 0.000 0.0048 0.9990 0.9990   1.16  1  1  8.7E-01
  3 :   0.00E+00 5.52E-04 0.000 0.0000 1.0000 1.0000   1.00  1  1  
iter seconds digits       c*x               b*y
  3      0.0   Inf  0.0000000000e+00  0.0000000000e+00
|Ax-b| =   0.0e+00, [Ay-c]_+ =   0.0E+00, |x|=  0.0e+00, |y|=  4.6e+05

Detailed timing (sec)
   Pre          IPM          Post
4.999E-03    2.200E-02    1.100E-02    
Max-norms: ||b||=0, ||c|| = 1000000,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 1.

ans =

    yalmiptime: 0.1580
    solvertime: 0.0410
          info: 'Successfully solved (SeDuMi-1.3)'
       problem: 0