There is a problem, actually a maximization problem, I solved it by CVX successfully (maybe I wrote the wrong code). But in fact, I can’t prove it’s a concave problem. So what’s the problem?
This problem is presented as below:

Oh! I’m so sorry! I found I forgot to specify β is the optimization variable. And I try to calculate its second-order derivative, it doesn’t satisfy the ≥ 0 condition.

In the future, you should more clearly state your question, including the optimization problem it pertains to. You said your object is to maximize Ou, in which case T_u would have nothing to do with that, and is just a “random image” posted along with the relevant one for Ou.

Thank you very much for your valuable advice, and for answering my question seriously! I will correct my faults to prevent similar problems from happening. Thank you once again!