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Constructing the value function for an Integer Linear Programme over a Cone

Williams, H. Paul (1996) Constructing the value function for an Integer Linear Programme over a Cone. Computational Optimization and Applications, 6 (1). pp. 15-26. ISSN 0926-6003

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Abstract

The value function of an Integer Programme is the optimal objective value expressed as a function of the right-hand-side coefficients. For an Integer Programme over a Cone (ILPC) this takes the form of a Chvátal Function which is built up from the operations of taking non-negative linear combinations and integer round-up. A doubly recursive procedure for calculating such a value function is given. This is illustrated by a small numerical example. It is also shown how the optimal solution of an ILPC can be obtained as a function of the right-hand-side through this recursion. The connection with the Group optimization representation of an ILPC is also given together with a discussion of the difficulty of calculating the value function for a general Integer Programme.

Item Type: Article
Official URL: http://www.springer.com/mathematics/journal/10589
Additional Information: © 1996 Kluwer Academic Publishers
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Research centres and groups > Management Science Group
Departments > Management
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 24 Jan 2011 10:57
URL: http://eprints.lse.ac.uk/31595/

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