A generalization of Fenchel duality theory. (English) Zbl 0568.90092
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.
Keywords:
theorem of the alternative; separation theorem; extension of Fenchel duality theory; fractional extremum problems; conjugate function; decompositionReferences:
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