# Examples of non trivial problems in this structure.

I'm looking for examples of non trivial problems that match with the follow structure. Let the function $$g: U \times V \rightarrow \mathbb{R}$$, where $U$ and $V$ are complex vetorial spaces of dimension, respectivaly, $n \times n$ and $n \times 1$. Then, we let the second function $$f(u_{i}) = \min(g(u_{i},v_{i})) \ \forall\ v_{i} \in V$$, where $u_{i} \in U$. Now, the main objective is find solutions $u_{k}$ of $f$ (same approximate) including the restriction that $\nexists \ v \in V \ / \ g(u_{k},v) = 0$.

Does anyone know any example?