Abstract
A conjecture of Deutsch, Li, and Swetits on duality relationships among three optimization problems is shown to hold true. The proof relies on a reformulation of one of the problems in a suitable product space, to which then a version of the classical Fenchel duality theorem applies.
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References
Deutsch, F., Li, W., and Swetits, J., Fenchel Duality and the Strong Conical Hull Intersection Property, Journal of Optimization Theory and Applications, Vol. 102, pp. 681–695, 1999.
Barbu, V., and Precupanu, T., Convexity and Optimization in Banach Spaces, 2nd Edition, D. Riedel Publishing Company, New York, New York, 1985.
Zeidler, E., Nonlinear Functional Analysis and Its Applications, Vol. 3: Variational Methods and Optimization, Springer Verlag, New York, New York, 1985.
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Bauschke, H.H. Proof of a Conjecture by Deutsch, Li, and Swetits on Duality of Optimization Problems. Journal of Optimization Theory and Applications 102, 697–703 (1999). https://doi.org/10.1023/A:1022610425736
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DOI: https://doi.org/10.1023/A:1022610425736