Abstract
This paper deals with an extention 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.
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Communicated by I. Galligani
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Beoni, C. A generalization of Fenchel duality theory. J Optim Theory Appl 49, 375–387 (1986). https://doi.org/10.1007/BF00941068
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DOI: https://doi.org/10.1007/BF00941068