Suppose we wanted to solve the following optimization problem: $$\inf_{x \geq 0}\sup_{y \in [0, 1];\ z > 0} f(x, y, z),$$ where $f(x, y, z)$ is some objective function with a closed form that can be specified in terms of parameters $x$, $y$, $z$. How would we implement this optimization, say using the Python programming language?
I am only vaguely familiar with implementing optimization in the Bayesian setting (eg using variational inference) or by a grid search. But I do not think Bayesian optimization works here as there are any priors here (I could be wrong though) and I'm not quite sure how to discretize these parameters in a reasonable way.
(The motivation for the optimization problem above comes from my personal study of robust optimization models from the paper https://arxiv.org/pdf/1908.05659.pdf.)