Multiobjective Fractional Programming Problems and Second Order Generalized Hybrid Invexity Frameworks

Ram Verma

doi:10.19139/soic.v2i4.92

Abstract

In this paper, first generalized sufficient efficiency conditions for multiobjective fractional programming based on the generalized hybrid invexities are developed , and then efficient solutions to multiobjective fractional programming problems are established. The obtained results generalize and unify a wide range of investigations in the literature.

Highlights

Mishra and Rueda [11] introduced higher order generalized invexity and duality models in mathematical programming, while Mangasarian [8] focused on the second order duality for a conventional nonlinear programming problem, where the approach is based on constructing a second order dual problem by taking linear and quadratic approximations of the objective and constraint functions for an arbitrary but fixed point leading to the Wolfe dual model for the approximated
Verma [22] investigated a general framework for a class of (ρ, η, θ)−invex functions to examine some parametric sufficient efficiency conditions for multiobjective fractional programming problems for weakly ε−efficient solutions
We established several results on multiobjective fractional programming problems based on the generalized hybrid (Φ, ρ, η, ζ, θ)−invexities and on efficient solutions to the multiobjective fractional programming problems

Summary

Introduction

Mishra and Rueda [11] introduced higher order generalized invexity and duality models in mathematical programming, while Mangasarian [8] focused on the second order duality for a conventional nonlinear programming problem, where the approach is based on constructing a second order dual problem by taking linear and quadratic approximations of the objective and constraint functions for an arbitrary but fixed point leading to the Wolfe dual model for the approximated. Verma [24] investigated the second order (ρ, η, θ)−invexities to the context of parametric sufficient optimality conditions in semiinfinite discrete minimax fractional programming. Verma [22] investigated a general framework for a class of (ρ, η, θ)−invex functions to examine some parametric sufficient efficiency conditions for multiobjective fractional programming problems for weakly ε−efficient solutions. The results established in this communication, generalize (and unify) the results on general sufficient efficiency conditions for multiobjective fractional programming problems based on the hybrid invexity of functions, and generalize second order invexity results to more general settings. For more details on generalized efficiency and efficiency results and applications, we recommend the reader [1]-[41] This submission is organized as follows: the introductory section deals with a brief historical development for the multiobjective fractional mathematical programming, while emphasizing the roles of the generalized invex functions.

Hybrid Invexities

Concluding Remarks