A generalization of Fenchel duality theory (Q1061016)

This paper deals with an extension of Fenchel duality theory to fractional extremum problems, i.e., problems having a fractional objective function. The main result is obtained by regarding the classic Fenchel theorem as a decomposition property for the extremum of a sum of functions into a sum of extrema of functions, and then by extending it to the case where the addition is replaced by the quotient. This leads to a generalization of the classic concept of conjugate function. Several remarks are made about the conceivable further generalizations to other kinds of decomposition.