\(E\)-univex sets, \(E\)-univex functions and \(E\)-differentiable \(E\)-univex programming (Q2095501)

A new concepts of \(E\)-univex sets and \(E\)-univex functions are introduced. The concepts generalize some concepts of generalized convexity published in the literature. Further the concept of differentiability is extended to \(E\)-univex functions and called \(E\)-differentiability. \(E\)-differentiable nonlinear optimization problems are formulated and an \(E\)-convex version of Karush-Kuhn-Tucker necessary optimality conditions are proved. The introduced new concepts and results are explained on small numerical examples. Further research in the area of \(E\)-univexity is shortly outlined in the conclusions of the paper.