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

Abstract

The parametrically generalized sufficient efficiency conditions for multiobjective fractional programming based on the hybrid (Φ,Ψ,Ï,ζ,θ)−invexities are developed and then efficient solutions to the multiobjective fractional programming problems are established. Plus, the obtained results on sufficient efficiency conditions are generalized to the case of the ϵ−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,Ï,ζ,θ)−invexity frameworks.