Some Properties of Semi-E-Convex Function and Semi-E-Convex Programming

摘要

IN Ref 1 ,Yang shows that some of the results obtained in Ref. 2 on E-convex programming are incorrect, in Ref 3,Chen introduce semi-E-convex functions to correct the main results in Ref.2, in Ref 4,Duca and Lupsa show that the results obtained in Ref. 2 concerning the characterization of an Econvex function f in terms of its E-epigraph are incorrect. And give some characterizations of Econvex functions using two notion of epigraph (epiE(f) and epi(f)). In this note, some new properties of semi-E-convex functions are discussed, and new characterizations of semi-E-convex functions using a new epigraph of epi (f) and slack 2-convex set are proposed, more new results of semi E-convex programming are given.