How to provide a starting point for BMIBNB in yalmip?

[namrata-kundu]

I have a non-convex optimization problem and bmibnb takes a very long time to run and times out. Is there a way to provide a custom starting point such that it can converge to the optimal solution faster?

[johanlofberg]

https://yalmip.github.io/warmstart

Most likely though, the problem is not to find a good solution (or even the globally optimal one) but proving it is optimal by closing the gap from below.

[namrata-kundu]

Hello, just checking in to see if there's any update here. I would highly appreciate if you could please kindly let me know if this is an issue on yalmip's side or if I'm missing something here. It'll help me move forward.
Thanks for all your help.

[johanlofberg]

The numerics here is just simply brutal, so not surprised that weird tings happen

For instance, trying to solve the integer-relaxed problem using fmincon, and it shows horrible logs, both cold- and warm-starting

sol = optimize(Constraints,objective, sdpsettings('solver','fmincon','usex0',0,'relax',1))

If you turn on display so you see the logs from the linear relaxations too, you will see that the solver constantly is complaining about poor numerics (large bounds)

sol = optimize(Constraints,objective, sdpsettings('solver','bmibnb','verbose',3))

As far as I can see in your model, you lack bounds on many of the decision variables, and this will destroy the numerics in a global b&b solver, and in theory typically make the problem unsolvable using a b&b solver as the branching domain is infinite. You will have to fix this before anything can be said or done

[johanlofberg]

Also make sure you are running the develop branch, and make sure you pull for changes, as I am fixing various robustness issues popping up on this bad model

[johanlofberg]

The model is strange

This

for i=1:size(npp,2)-1
    con1= npp(i) <= (npp(i+1)-epsilon);
    Constraints1 = [Constraints1, con1]:'constraints1';
end

immediately says there can be at most 1 zero in npp, which renders the very complicated nnz(npp) >= 10 which forces the use of integer variables and a hard MINLP model, effectively redundant

[johanlofberg]

BTW, this

a = cell(size(new_f,2),1);
b = cell(size(new_f,2),1);
c = cell(size(new_f,2),1);
for i=1:size(new_f,2)
    a{i} = sdpvar(1,1); 
    b{i} = sdpvar(1,1); 
    c{i} = sdpvar(1,1); 
    values = [a{i}; b{i}; c{i}];
    rho = [rho values];
end

is a complicated way of doing

n = size(new_f,2);
a = sdpvar(1,n)
b = sdpvar(1,n)
c = sdpvar(1,n)
rho = [a;b;c];