Hybrid (Φ,Ψ, ρ, ζ, θ)−invexity frameworks and efficiency conditions for multiobjective fractional programming problems

Abstract

The parametrically generalized sufficient efficiency conditions for mult iobjective fractional programming based on the hybrid (Φ,Ψ,ρ,ζ,θ)-invexities are developed and then efficient solutions to the multiobjective fractional programming problems are established. Plus, the obtained results on sufficient efficiency condition s are generalized to the case of the ǫ-efficient solutions. The results thus obtained generalize and unify a wider range of investigations on the theory and applications to the multiobjective fractional programming based on the hybrid (Φ,Ψ,ρ,ζ,θ)-invexity frameworks.