Abstract
In Ref 1, Yang shows that some of the results obtained in Ref. 2 on E-convex programming are incorrect, but does not prove that the results which make the connection between an E-convex function and its E-epigraph are incorrect. In this note, we show that the results obtained in Ref. 2 concerning the characterization of an E-convex function f in terms of its E-epigraph are incorrect. Afterward, some characterizations of E-convex functions using a different notion of epigraph are given.
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Communicated by X.Q. Yang
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Duca, D.I., Lupşa, L. On the E-Epigraph of an E-Convex Function. J Optim Theory Appl 129, 341–348 (2006). https://doi.org/10.1007/s10957-006-9059-y
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DOI: https://doi.org/10.1007/s10957-006-9059-y