Duality in MIP. Generating Dual Price Functions Using Branch-and-Cut

Elena V. Pachkova

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Ingår i: Nordic MPS 2004. The Ninth Meeting of the Nordic Section of the Mathematical Programming Society

Linköping Electronic Conference Proceedings 14:5, s. 73-87

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Publicerad: 2004-12-28


ISSN: 1650-3686 (tryckt), 1650-3740 (online)


This presentation treats duality in Mixed Integer Programming (MIP in short). A dual of a MIP problem includes a dual price function F; that plays the same role as the dual variables in Linear Programming (LP in the following).

The price function is generated while solving the primal problem. However; different to the LP dual variables; the characteristics of the dual price function depend on the algorithmic approach used to solve the MIP problem. Thus; the cutting plane approach provides non-decreasing and superadditive price functions while branch-and-bound algorithm generates piecewise linear; nondecreasing and convex price functions.

Here a hybrid algorithm based on branch-and-cut is investigated; and a price function for that algorithm is established. This price function presents a generalization of the dual price functions obtained by either the cutting plane or the branch-and-bound method.


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