Abstract
The relation of two mathematical programs—the so-called primal, (P) and dual, (D)—Are studied when (P) is a maximization of the minimum of two functions and (D) is the minimization of the maximum of two functions, and the function-pair of (D) are derived by certain, conjugate-like operators from that of (P). It is demonstrated that the weak duality holds when at least one of the pair is continuous. When further premises are met the strong duality is proved. From these results the usual Fenchel-duality may be deducted as well as few other primal-dual pairs.
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Flachs, J., Pollatschek, M.A. Duality theorems for certain programs involving minimum or maximum operations. Mathematical Programming 16, 348–370 (1979). https://doi.org/10.1007/BF01582120
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DOI: https://doi.org/10.1007/BF01582120