In optimization theory, the feasible region of a problem is the set of all values of its decision variables that satisfy every constraint. A point in the feasible region is a feasible solution. Points outside it cannot be optimal, regardless of the value of the objective function.
For a linear programming problem written as 
together with equality and bound
constraints, the feasible region is an intersection of half-spaces
and affine subspaces, and is therefore a convex set.
It is a convex polyhedron and may be empty,
unbounded, or lower-dimensional. Nonlinear constraints can instead produce disconnected
or nonconvex feasible regions.
