Trying to solve non-convex problem globally but only 'bmibnb' works

[David1]

Dear Professor Löfberg,

I'm trying to solve the following (non-convex) optimization problem with as many global solvers as possible (I know only about bmibnb, baron, scip).

But only the bmibnb solver works for me.

clear;
close all;
clc;


n = 7;
d = 2;


A = rand(n,d);
b = rand(n,1);
x = sdpvar(d,1);


Objective = norm(A*x-b,1);
cons = [x'*x==1];
options = sdpsettings('solver','bmibnb');


sol= optimize(cons,Objective, options);
sol.info  

When I try baron or scip it writes 'Solver not found'.

I checked this link for baron solver:

https://minlp.com/baron-downloads

and when downloaded (for Windows 64 bit) it only downloaded baron.exe and some more dll files. I was actually looking for baron.m so I can run it through yalmip.

Can you please tell me how can I make baron and scip work on yalmip?

also, are there more global solvers (for non-convex problems) that I can try?

and last, can you tell me which one is considered the fastest? When I ran the above code with big n (say n=1000) it took a long time to solve the problem (that's why I wanted to check more solvers).

Thank you very much!

[Johan Löfberg]

You have to have the baron matlab interface, it won't work without that. For scip, you have to install OPTI Toolbox

However, if you're really only interested in d=2 and n huge, simply grid the unit-circle and compute the function value for each case. You will never be able to beat that.

[David1]

Thank you for your answer.

Just installed both baron matlab interface and OPTI Toolbox.

still can't run any of them.

for 'baron' I get 'Licensing error' (eventhough I signed up with my university email - Haifa university. I'm not sure if it accepted it as a legit email)

for 'scip' I get 'Solver not applicable (scip)'. don't understand why (I put the mex file that I installed in yalmip's folder 'solvers').

Are there any other solvers that I can try?

no, I'm actually interested on any d. d=2 was only an example.

[Johan Löfberg]

regarding baron, sounds like you haven't placed the license file in the correct place (or your problem is too large for your license)

for scip, I think you have to specify scip-nl as the solver

You absolutely don't put any files in YALMIPs folders. Keep different packages apart, otherwise you will have a complete chaos they day you must upfdate yalmip etc.