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IBM Journal of Research and Development  
Volume 31, Number 2, Page 206 (1987)
Mathematics and Computing
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The group problem and integer programming duality

by E. L. Johnson
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.
Related Subjects: Mathematics; Programming, programs, and programming languages