Article | Nordic MPS 2004. The Ninth Meeting of the Nordic Section of the Mathematical Programming Society | Duality in MIP

Title:
Duality in MIP
Author:
Elena V. Pachkova: Copenhagen University, Denmark
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Full text (pdf)
Year:
2004
Conference:
Nordic MPS 2004. The Ninth Meeting of the Nordic Section of the Mathematical Programming Society
Issue:
014
Article no.:
020
No. of pages:
1
Publication type:
Abstract
Published:
2004-12-28
Series:
Linköping Electronic Conference Proceedings
ISSN (print):
1650-3686
ISSN (online):
1650-3740
Publisher:
Linköping University Electronic Press; Linköpings universitet


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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 nondecreasing 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.

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

Author:
Elena V. Pachkova
Title:
Duality in MIP
References:
No references available

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

Author:
Elena V. Pachkova
Title:
Duality in MIP
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