Optimality conditions and duality for E-differentiable multiobjective programming involving V-E-type I functions
Najeeb Abdulaleem, Savin Treanţă
Abstract
Abstract In this paper, we introduce a new concept of sets and a new class of functions called $$\alpha$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> - E -invex sets and V-E-preinvex functions. Furthermore, a new concept of generalized convexity is introduced for (not necessarily) differentiable vector optimization problems. Namely, the concept of V - E -type I functions is defined for E -differentiable vector optimization problem. A number of sufficiency results are established under various types of (generalized) V - E -type I requirements. Moreover, several E -duality theorems in the sense of Mond–Weir are proved under appropriate (generalized) V - E -type I functions.