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A Comparison of Mixed-Integer Programming Models for Nonconvex Piecewise Linear Cost Minimization Problems

By Keely L. Croxton, Bernard Gendron and Thomas L. Magnanti


We study a generic minimization problem with separable nonconvex 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.Piecewise Linear, Integer Programming, Linear Relaxation, Lagrangian Relaxation

DOI identifier: 10.1287/mnsc.49.9.1268.16570
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