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The group problem and integer programming duality

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1 Author(s)
Ellis L. Johnson ; IBM Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 1059, USA

Some duality results for integer programming based on subadditive functions are presented first for linear programs and then for the group problem. A similar result for the knapsack problem is given and then a relationship between facets for the group relaxation and facets of the knapsack problem is given. The mixed integer cyclic group problem is then considered and a dual problem given. A common theme is to try to characterize the strongest possible dual problem or equivalently the smallest possible cone of subadditive functions.

Note: The Institute of Electrical and Electronics Engineers, Incorporated is distributing this Article with permission of the International Business Machines Corporation (IBM) who is the exclusive owner. The recipient of this Article may not assign, sublicense, lease, rent or otherwise transfer, reproduce, prepare derivative works, publicly display or perform, or distribute the Article.  

Published in:

IBM Journal of Research and Development  (Volume:31 ,  Issue: 2 )