Abstract
Following the idea of the conjecture for semi-infinite programming in a paper by Kortanek and Zhang, recently published in Optimization, in this paper we show that the Fourier–Motzkin elimination is not needed in the study of the strong duality and dual pricing properties for semi-infinite programming. We also prove several new results on the strong duality and dual pricing properties. Specifically, we propose a new subspace, under which the strong duality property holds. We give a necessary and sufficient condition for the dual pricing property to hold under this subspace, which is further used to examine the examples presented in the Basu–Martin–Ryan paper.
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I would like to thank an anonymous referee for the useful comments and suggestions.
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Communicated by Vaithilingam Jeyakumar.
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Zhang, Q. Strong Duality and Dual Pricing Properties in Semi-Infinite Linear Programming: A non-Fourier–Motzkin Elimination Approach. J Optim Theory Appl 175, 702–717 (2017). https://doi.org/10.1007/s10957-017-1184-2
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DOI: https://doi.org/10.1007/s10957-017-1184-2