How to use the log sum exp function to model this constraint ?

[JackJack]

Dear Professor Johan,

How can I model the following log sum exp constraint using the logsumexp function 


I have read the document but due to my background as an engineer and not a mathematician, I find it difficult to understand.


https://yalmip.github.io/tutorial/exponentialcone/


I hope you can provide some assistance.

Thank you very much and best regards.

[JackJack]

% Define variables

x1 = sdpvar(1);

x2 = sdpvar(1);

x3 = sdpvar(1);

x4 = sdpvar(1);

t = sdpvar(1);

% Define constants (you may need to assign specific values)

c1 = 9; % Example value, adjust as needed

c2 = 100; % Example value, adjust as needed

% Set up the constraint using logsumexp

constraint = logsumexp([x1 - 2*x2 + log(c1), x3 - 6*x4 - log(c2)]) <= t;

% Define the objective

objective = t;

% Set up the optimization problem

ops = sdpsettings('solver', 'mosek'); % Specify MOSEK as the solver

problem = optimize(constraint, objective, ops);

% Check the result

if problem.problem == 0

disp('Solved successfully');

optimal_t = value(t);

optimal_x = [value(x1), value(x2), value(x3), value(x4)];

disp(['Optimal t: ', num2str(optimal_t)]);

disp('Optimal x values:');

disp(optimal_x);

else

disp('Problem encountered');

end Particularly, this code give me a bunch of strange error.

[Johan Löfberg]

You would have to be way more specific than "a bunch of strange error"

The model is ill-posed though as you can make the vector go to -inf meaning exp will go to 0 meaning log and thus objective will go to -inf

[JackJack]

Thank you, I have checked again. The strange error is not YALMIP related. The root cause is that because I install both YALMIP and CVX and both of them has the logsumexp function so they are conflicting each other. By uninstalling CVX, everything works fine.

Therefore, my question is now more related to the syntax of of the logsumexp command.

That is "Does this YALMIP syntax (above) correctly represent the mathematical constraint (below) ?"

 



Thank you and best regard !

[Mark L. Stone]

Rather than uninstalling CVX, you can just get rid of its `logsumexp`, which is just a useless function which says that you should use `log_sum_exp`.

[Johan Löfberg]

yes https://yalmip.github.io/command/logsumexp/

[JackJack]

Thank you so much Professor Mark and Professor Johan for your support !

@Johan: Are there anyway to contribute to the YALMIP documentation so that it could be clearer ?
I hope to do so because I see that YALMIP is very good but sometime the document is not rich enough.

[Johan Löfberg]

Just make a pull-request on the repo