Let $G=(V,E)$ be a graph (i.e. an undirected simple finite graph). We say that a vertex cover $V'$ of $G$ is non-reducible if any $V''$ with $V''\subsetneq V'$ is not a vertex cover of $G$. We say that a non-reducible vertex cover $V'$ of $G$ is maximal if for all non-reducible vertex cover $V''$ of $G$ we have $|V''|\le |V'|$. Note that the minimum vertex cover is non-reducible, but of course not necessarily maximal.
What is know about the (time)-complexity of finding a maximal non-reducible vertex cover?
Is there anything known for hypergraphs with multiple edges?