Feasible region
（重定向自Feasible set）
![A problem with five linear constraints (in blue, including the non-negativity constraints). In the absence of integer constraints the feasible set is the entire region bounded by blue, but with integer constraints it is the set of red dots.](/Images/godic/202501/12/IP_polytope_with_LP_relaxation5506.png")
![A closed feasible region of a linear programming problem with three variables is a convex polyhedron.](/Images/godic/202501/12/3dpoly.svg5506.png")
![](/Images/godic/202501/12/Linear_Programming_Feasible_Region.svg5506.png")
![A bounded feasible set (top) and an unbounded feasible set (bottom). The set at the bottom continues forever towards the right.](/Images/godic/202501/12/Bounded_unbounded.svg5506.png")
In mathematical optimization, a feasible region, feasible set, search space, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints. This is the initial set of candidate solutions to the problem, before the set of candidates has been narrowed down.