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Duality in mathematics and linear and integer programming

Williams, H.P. (1996) Duality in mathematics and linear and integer programming Journal of Optimization Theory and Applications, 90, (2), pp. 257-278. (doi:10.1007/BF02189998).

Record type: Article


Linear programming (LP) duality is examined in the context of other dualities in mathematics. The mathematical and economic properties of LP duality are discussed and its uses are considered. These mathematical and economic properties are then examined in relation to possible integer programming (IP) dualities. A number of possible IP duals are considered in this light and shown to capture some but not all desirable properties. It is shown that inherent in IP models are inequality and congruence constraints, both of which give on their own well-defined duals. However, taken together, no totally satisfactory dual emerges. The superadditive dual based on the Gomory and Chvátal functions is then described, and its properties are contrasted with LP duals and other IP duals. Finally, possible practical uses of IP duals are considered.

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Published date: 1996
Organisations: Operational Research


Local EPrints ID: 29654
ISSN: 0022-3239
PURE UUID: 8d6eb1e2-93b5-4ef9-b26d-b6525027be40

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Date deposited: 20 Dec 2006
Last modified: 17 Jul 2017 15:57

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Author: H.P. Williams

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