The cutting-plane method for solving 0-1 integer programs, first introduced for the traveling salesman problem by and generalized to other integer programs by , takes advantage of this multiplicity of possible relaxations by finding a sequence of relaxations that more tightly constrain the solution space until eventually an integer solution is obtained. This method starts from any relaxation of the given program, and finds an optimal solution using a linear programming solver. If the solution assigns integer values to all variables, it is also the optimal solution to the unrelaxed problem. Otherwise, an additional linear constraint (a "cutting plane" or "cut") is found that separates the resulting fractional solution from the convex hull of the integer solutions, and the method repeats on this new more tightly constrained problem.