How to minimize a loss function that is dependent on itself through the coefficients?

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For an optimization problem I am solving, I have the following problem.

We have to minimize loss function $f$, which is dependent on a coefficient vector $\theta$, $A$, and $B$. Now $B$ is dependent on the maximum of $f$. I am unsure what kind of algorithm is used. I am guessing some kind of fixed-point algorithm.

An example I'm thinking of would find start with some value for $B$, use gradient descent on $\theta$, and reiterate until some criteria are met. But I hope there is something better.

$\color{magenta}{\star}$ What type of algorithm would be used for such a problem where the function is dependent on coefficients that are dependent on the function itself? And, possibly, what would be the requirements for it to converge?


I am fairly sure it is not possible to define a function in the way I did, however maybe someone is familiar with similar problems and could give me a source for functions/ optimization problems like this one.