A Comparison of Mixed-Integer Programming Models for Non-Convex Piecewise Linear Cost Minimization Problems
Author(s)Croxton, Keely L.; Gendon, Bernard; Magnanti, Thomas L.
We study a generic minimization problem with separable non-convex piecewise linear costs, showing that the linear programming (LP) relaxation of three textbook mixed integer programming formulations each approximates the cost function by its lower convex envelope. We also show a relationship between this result and classical Lagrangian duality theory.
Massachusetts Institute of Technology, Operations Research Center
Operations Research Center Working Paper;OR 363-02
piecewise-linear, integer programming, linear relaxation, Lagrangian relaxation.