in this paper, using clarke’s generalized directional derivative and di-invexity we introduce new concepts of nonsmooth k-α-di-invex and generalized type i univex functions over cones for a nonsmooth vector optimization problem with cone constraints. we obtain some sufficient optimality conditions and mond-weir type duality results under the foresaid generalized invexity and type i cone-univexi...

In this paper, using Clarke’s generalized directional derivative and dI-invexity we introduce new concepts of nonsmooth K-α-dI-invex and generalized type I univex functions over cones for a nonsmooth vector optimization problem with cone constraints. We obtain some sufficient optimality conditions and Mond-Weir type duality results under the foresaid generalized invexity and type I cone-univexi...

In this paper, we introduce a new class of generalized dI-univexity in which each component of the objective and constraint functions is directionally differentiable in its own direction di for a nondifferentiable multiobjective programming problem. Based upon these generalized functions, sufficient optimality conditions are established for a feasible point to be efficient and properly efficien...

In this paper, a new class of second order ( , )   -univex and second order ( , )   pseudo univex function are introduced with example. A pair Mond-Weir type second order mixed symmetric duality for multiobjective nondifferentiable programming is formulated and the duality results are established under the mild assumption of second order ( , )   univexity and second order pseudo univexity...

Three approaches of second order mixed type duality are introduced for a nondifferentiable multiobjective fractional programming problem in which the numerator and denominator of objective function contain square root of positive semidefinite quadratic form. Also, the necessary and sufficient conditions of efficient solution for fractional programming are established and a parameterization tech...

The aim of the present paper is to obtain a number of Kuhn-Tucker type sufficient optimality conditions for a feasible solution to be an efficient solution under the assumptions of the new notions of weak strictly pseudo quasi α-univex, strong pseudo quasi α-univex, and weak strictly pseudo α-univex vector valued functions. We also derive the duality theorems for Mond-Weir and general Mond-Wei...

whereAn is the n-fold product of the σ-algebraA of subsets of a given set X ,Fi,Gi, i∈ p ≡ {1,2, . . . , p}, and Hj , j ∈ q, are real-valued functions defined on An, and for each i ∈ p, Gi(S) > 0 for all S∈An such that Hj(S) 0, j ∈ q. This paper is essentially a continuation of the investigation that was initiated in the companion paper [6] where some information about multiobjective fractional...

The purpose of this paper is to develop a fairly large number of sets of global parametric sufficient optimality conditions under various generalized (F, b, φ, ρ, θ)univexity assumptions for a continuous minmax fractional programming problem involving arbitrary norms.