feasible region

The set of every $x$ that satisfies all of a problem's constraints at once.

The feasible region (or feasible set) $\mathcal F$ is the set of every decision-variable value $x$ that satisfies all of a problem's constraints simultaneously: $\mathcal F = \{x : g_i(x)\le0\ \forall i,\ h_j(x)=0\ \forall j\}$ . A point in $\mathcal F$ is feasible; a problem with $\mathcal F=\varnothing$ is infeasible. Optimization only ever compares objective values among feasible points.

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