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).


Full text not available from this repository.


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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1007/BF02189998
ISSNs: 0022-3239 (print)
Organisations: Operational Research
ePrint ID: 29654
Date :
Date Event
Date Deposited: 20 Dec 2006
Last Modified: 16 Apr 2017 22:21
Further Information:Google Scholar
URI: http://eprints.soton.ac.uk/id/eprint/29654

Actions (login required)

View Item View Item