I have a combinatorial problem of the form below
$$\max_{x_t\in \{-1,1\}}\min_{x_i\in \{-1,1\}, i\in \{1,...,n\}-S-t} x^\mathsf{T} R x$$
where $R$ is a $n\times n $ matrix with nonnegative elements and some $x_i$ for $i \in S\subset \{1,...,n\} $ are known.
My question is:
What is this problem in combinatorial optimization literature? I saw some problems as SAT, or CSP, etc. But I don't know what is the name for this problem. And is there any approximate solution for this problem?