We consider two generalized Minty vector variational-like inequalities and investigate the relations between their solutions and vector optimization problems for non-differentiable α-invex functions.

In this paper, we introduce and study some new classes of invex sets preinvex functions with respect to an arbitrary function k the bifunction ?(.,.); which are called generalized functions. These nonconvex include function, convex k-convex as special cases. We properties It is shown that minimum on can be characterized by a class variational inequalities, directional variational-like inequalit...

In section 4.1 a new class of higher order (F,ρi, σj)type I functions are introduced for a vector minimization problem. Various known generalized invex functions such as type-I, second order type-I and second order (F,ρi,σj)-type I are particular cases of higher order (F, ρi, σj)-type I functions. This class of functions is used to establish higher order duality results for a nondifferentiable ...

In the present paper the definition of invexity for continuous functions is extended to invexity of order m which is further generalized to ρ-pseudoinvexity type I of order m, ρ-pseudoinvexity type II of order m, as well as ρ-quasi invexity type I of order m and ρ-quasiinvexity type II of order m. The central objective of the paper is to study variational problem where the functionals involved ...

E-convex function was introduced by Youness 1 and revised by Yang 2 . Chen 3 introduced Semi-E-convex function and studied some of its properties. Syau and Lee 4 defined E-quasi-convex function, strictly E-quasi-convex function and studied some basic properties. Fulga and Preda 5 introduced the class of E-preinvex and E-prequasi-invex functions. All the above E-convex and generalized E-convex f...

( , ) ρ Φ − invexity has recently been introduced with the intent of generalizing invex functions in mathematical programming. Using such conditions we obtain new sufficiency results for optimality in multiobjective programming and extend some classical duality properties.

In this paper, a generalization of convexity, namely V -rinvexity, is considered in the case of nonlinear multiobjective programming problems where the functions involved are differentiable. The assumptions on Pareto solutions are relaxed by means of V -r-invex functions. Also some duality results are obtained for such optimization problems.