Closely related (although not equivalent) to minimax optimization problems is the following:
$$\min_{x \in \Omega} \min_{i=1,...,q} f_i (x).$$ Here, $\Omega \subset \Bbb R^n$ and $f_i: \Bbb R^n \to \Bbb R$ is continuously differentiable. I am looking for references on algorithms for this kind of problems. Specifically, I am interested in steepest- descent -like methods. Can you suggest a good reference/survey?