Solution set

In mathematics, a solution set is the set of values that satisfy a given set of equations or inequalities.

For example, for a set ${\displaystyle \{f_{i}\}}$ of polynomials over a ring ${\displaystyle R}$, the solution set is the subset of ${\displaystyle R}$ on which the polynomials all vanish (evaluate to 0), formally

${\displaystyle \{x\in R:\forall i\in I,f_{i}(x)=0\}}$

The feasible region of a constrained optimization problem is the solution set of the constraints.