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

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

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Author: Croxton, Keely L.; Gendon, Bernard; Magnanti, Thomas L.
Publisher: Massachusetts Institute of Technology, Operations Research Center
Date Issued: 2002-07
Abstract:
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.
URI: http://hdl.handle.net/1721.1/5233
Series/Report no.: Operations Research Center Working Paper;OR 363-02
Keywords: piecewise-linear, integer programming, linear relaxation, Lagrangian relaxation.

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