SDPT3-Maximum iterations or time limit exceeded

[XM XM]

Hi Johan,

I am working with the following code:

r = sdpvar(len_r, 1); %

r_mean = ones(len, 1); % this is a user-defined value

e == sdpvar(M, 1);

Constraints = [-1 <= r <= r, others, e == R'\(r - r_mean) ] % all constraints are linear 

Objective = e' * e;

options = sdpsettings('solver','sdpt3');

sol = solvesdp(Constraints,Objective, options);

if sol.problem == 0

 solution = sparse(double(r));

else

 display('Something went wrong!');

 sol.info;

 yalmiperror(sol.problem);

end

I am now working on a problem of the size 45000 (in stead of 70000) and use sdpt3 as the solver. R here is sparse, as nnz(R)/numel(R) = 5.6667*e-4. I actually know the real r values and the purpose of this work is to show the solved optimal solution is very close to the real r values. I have checked the real r values satisfies all constraints and under this r, e'*e = 159, a satisfactory result.

However, when I am running the code, I encounter the error message of "Maximum iterations or time limit exceeded (SDPT3-4)". What do you think might be the problem? I saw in another post you said it might be because the problem is numerically ill-posed so that increase the sdpt3.maxit may not help. But I cannot see it is the case in my problem. Thanks!

[Mark L. Stone]

Try MOSEK if you have access to it.  I don't recall any problem for which SDPT3 or SeDuMi did better than MOSEK. But I have seen many problems which MOSEK solved, but SDPT 3 and//or SeDumI ran into numerical problems.

[Mark L. Stone]

Well, actually now that I see you just have a convex QP, you could use cplex (set numerical emphasis on) or GUROBI.  MOSEK as well. I'd pick any of those over SDPT3 or SeDuMi for your problem.

[Mark L. Stone]

I don't  know what solvers you have installed.  What solver does YALMIP pick if you don't specify solver?

[Mark L. Stone]

Did you try the obvious thing of increasing maximum number of iterations and time limit?  What was the SDPT3 output looking like?  Was there evidence of progress?  Did it just quit without (before) saying it ran into numerical troubles?

[XM XM]

Hi Mark, thanks for your comments! I only use SDPT3 as the solver because I did not install cplex or gurobi on my personal laptop. I will try Gurobi.

[XM XM]

Hi Mark, I tried Gurobi. It takes only 10 seconds to solve the problem. At least for my problem, I think Gurobi works better than SDPT3. Thanks again for your help.

[Johan Löfberg]

Gurobi is commercial software, whereas sdpt3/sedumi are research proof-of-concepts codes for mixed semidefinite-second order cone programs, so it is very much excepted that cplex/gurobi/mosek are orders of magnitudes faster for large-scale problems. You get what you pay for (unless you are in academia...)