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), 257-278. (doi:10.1007/BF02189998).

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Original Publication URL: http://dx.doi.org/10.1007/BF02189998

Description/Abstract

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
ISSNs: 0022-3239 (print)
Related URLs:
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: University Structure - Pre August 2011 > School of Mathematics > Operational Research
ePrint ID: 29654
Date Deposited: 20 Dec 2006
Last Modified: 27 Mar 2014 18:18
URI: http://eprints.soton.ac.uk/id/eprint/29654

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