DUALITY IN MATHEMATICS AND LINEAR AND INTEGER PROGRAMMING

Linear programming (LP) duality is examined in the context of other du alities 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 int eger programming (IF) dualities. A number of possible IP duals are con sidered 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 d uals. However, taken together, no totally satisfactory dual emerges. T he superadditive dual based on the Gomory and Chvatal functions is the n described, and its properties are contrasted with LP duals and other IP duals. Finally, possible practical uses of IP duals are considered .