On Cross Decomposition for Mixed-Integer Programming

Primal and dual decomposition procedures can lead – dependent on the structure of the problem – to efficient procedures for solving mixed—integer programming problems. Benders’ decomposition takes advantage of the primal structure of a problem by temporarily fixing the aggravating integer variables, while dual structures can be exploited by relaxing the complicating constraints in Lagrangian fashion and solving the Lagrangian dual with subgradient optimization, multiplier adjustment methods, or Dantzig-Wolfe decomposition.