Integer programming
![IP polytope with LP relaxation](/Images/godic/202501/20/IP_polytope_with_LP_relaxation3500.png")
![The graph of a strictly concave quadratic function is shown in blue, with its unique maximum shown as a red dot. Below the graph appears the contours of the function: The level sets are nested ellipses.](/Images/godic/202501/20/Max_paraboloid.svg3500.png")
An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear.