Problem with log_sum_exp using MOSEK solver


I am using Mosek, and I need to calculate log_sum_exp of continuous variables at some point. If I use the log_sum_exp function, the returned result is “Unbounded”, some constraints do not hold, and yet the status is “solved”. If I change the line of log_sum_exp, with its approximation ( max(x) ), I obtain the results I expected.

I cannot use the approximation for a larger scenario, and also I would not prefer to use a loose approximation for a convex function.

I wonder if there’s any bug fixes that you’re aware of, or any ideas about what causes this problem.


Does your formulation have any integer or binary variable declarations? If not, we can remove the MIDCP designation, which only serves to confuse matters.

I’ve removed the “Urgent” designation here, because frankly, as a volunteer-driven forum it’s entirely inappropriate to expect rapid response. What I would say, unfortunately, is that log_sum_exp uses the unsupported successive approximation approach, and as a result there really is no guarantee that it will work. (Indeed, we don’t guarantee that any model will be solved properly, but we have far more confidence in models that don’t use the successive approximation method.)

Yes there are binary declarations, and that is also the motivation for using MOSEK.

Thanks, for the warning. The urgency was due to a close deadline, but I will watch my tone next time. I did not intend to pressure anybody anyhow.

Would you have any suggestions for working around log_sum_exp?

No problem, irem, thanks for the response. I have to say that I have never tested using log_sum_exp and integer variables together. I’m afraid I don’t have a solution for you here. I don’t think CVX is going to work for you.

Thank you Michael. Just to clarify, the variables I use in log_sum_exp are continuous, however, the problem have other binary variables.

For the rest of the people who may have similar problems: I will use an iterative approach, and maybe later on I can share some indicators of performance, e.g. closeness to the optimal solution.

Thanks for your help and support. It is greatly appreciated.