Integer Linear Programming - Duality

Main Resource: Applied Mathematical Programming by Bradley, Hax, and Magnanti (Addison-Wesley, 1977), provided by MIT

A canonical form of duality of an Integer Linear Programming problem:

An easy relationship of mathematical symbols:
  - objective function:  MAX ↔ MIN
  - constraint in primal/duality ↔ variables in duality/primal
       ≤ ↔ ≥
       = ↔ unrestrained

Strong Duality Property: If the primal (dual) problem has a finite optimal solution, then so does the dual (primal) problem, and these two values are equal.
  - If primal problem has a finite optimal solution, then dual problem has a finite optimal solution.

  - If primal problem has an unbounded solution, then dual problem is infeasible.

  - If primal problem is infeasible, then dual problem is either infeasible or has an unbounded solution.