sufficiency and duality for a nonsmooth vector optimization problem with generalized $alpha$-$d_{i}$-type-i univexity over cones‎

Sufficiency and duality for a nonsmooth vector optimization problem with generalized $alpha$-$d_{I}$-type-I univexity over cones‎

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...

On optimality and duality for multiple-objective optimization under generalized type I univexity

On a Nonsmooth Vector Optimization Problem with Generalized Cone Invexity

and Applied Analysis 3 Definition 2.2 see 16 . Let ψ : R → R be a locally Lipschitz function, then ψ◦ u;v denotes Clarke’s generalized directional derivative of ψ at u ∈ R in the direction v and is defined as ψ◦ u;v lim sup y→u t→ 0 ψ ( y tv ) − ψ(y) t . 2.4 Clarke’s generalized gradient of ψ at u is denoted by ∂ψ u and is defined as ∂ψ u { ξ ∈ R | ψ◦ u;v ≥ 〈ξ, v〉, ∀v ∈ Rn}. 2.5 Let f : R → R b...

Higher-Order Minimizers and Generalized -Convexity in Nonsmooth Vector Optimization over Cones

In this paper, we introduce the concept of a (weak) minimizer of order k for a nonsmooth vector optimization problem over cones. Generalized classes of higher-order cone-nonsmooth (F, ρ)convex functions are introduced and sufficient optimality results are proved involving these classes. Also, a unified dual is associated with the considered primal problem, and weak and strong duality results ar...

Second-order optimality and duality in vector optimization over cones

In this paper, we introduce the notion of a second-order coneconvex function involving second-order directional derivative. Also, second-order cone-pseudoconvex, second-order cone-quasiconvex and other related functions are defined. Second-order optimality and Mond-Weir type duality results are derived for a vector optimization problem over cones using the introduced classes of functions.

Higher Order Duality for Vector Optimization Problem over Cones Involving Support Functions

In this paper, we consider a vector optimization problem over cones involving support functions in objective as well as constraints and associate a unified higher order dual to it. Duality result have been established under the conditions of higher order cone convex and related functions. A number of previously studied problems appear as special cases.