Optimality and duality for generalized fractional programming involving nonsmooth (F, ρ)-convex functions

AbstractUsing a parametric approach, we establish necessary and sufficient conditions and derive duality theorems for a class of nonsmooth generalized minimax fractional programming problems containing (F, ρ)-convex function

Optimality Conditions and Duality of Three Kinds of Nonlinear Fractional Programming Problems

Some assumptions for the objective functions and constraint functions are given under the conditions of convex and generalized convex, which are based on the F-convex, ρ-convex, and (F,ρ)-convex. The sufficiency of Kuhn-Tucker optimality conditions and appropriate duality results are proved involving (F,ρ)-convex, (F,α,ρ,d)-convex, and generalized (F,α,ρ,d)-convex functions

Optimality conditions and duality for nondifferentiable multiobjective programming problems involving d-r-type I functions

AbstractIn this paper, new classes of nondifferentiable functions constituting multiobjective programming problems are introduced. Namely, the classes of d-r-type I objective and constraint functions and, moreover, the various classes of generalized d-r-type I objective and constraint functions are defined for directionally differentiable multiobjective programming problems. Sufficient optimality conditions and various Mond–Weir duality results are proved for nondifferentiable multiobjective programming problems involving functions of such type. Finally, it is showed that the introduced d-r-type I notion with r≠0 is not a sufficient condition for Wolfe weak duality to hold. These results are illustrated in the paper by suitable examples

On nonsmooth multiobjective fractional programming problems involving (p, r)− ρ −(η ,θ)- invex functions

A class of multiobjective fractional programming problems (MFP) is considered where the involved functions are locally Lipschitz. In order to deduce our main results, we introduce the definition of (p,r)−ρ −(η,θ)-invex class about the Clarke generalized gradient. Under the above invexity assumption, sufficient conditions for optimality are given. Finally, three types of dual problems corresponding to (MFP) are formulated, and appropriate dual theorems are proved

Multiobjective Programming under Generalized Type I Invexity

AbstractIn this paper we extend a (scalarized) generalized type-I invexity into a vector invexity (V-type I). A number of sufficiency results are established using Lagrange multiplier conditions and under various types of generalized V-type I requirements. Weak, strong, and converse duality theorems are proved in the generalized V-invexity type I setting

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. Keywords: Vector optimization, Cones, Support Functions, Higher Order Duality

Generalized Convexity in Multiobjective Programming

AbstractFor the scalar programming problem, some characterizations for optimal solutions are known. In these characterizations convexity properties play a very important role. In this work, we study characterizations for multiobjective programming problem solutions when functions belonging to the problem are differentiable. These characterizations need some conditions of convexity. In differentiable scalar programming problems the concept of invexity is very important. We prove that it is also necessary for the multiobjective programming problem and give some characterizations of multiobjective programming problem solutions under weaker conditions. We define analogous concepts to those of stationary points and to the conditions of Kuhn–Tucker and Fritz–John for the multiobjective programming problem

Nonsmooth multiobjective optimization using limiting subdifferentials

AbstractIn this study, using the properties of limiting subdifferentials in nonsmooth analysis and regarding a separation theorem, some weak Pareto-optimality (necessary and sufficient) conditions for nonsmooth multiobjective optimization problems are proved