Mathematical Programming Based on Sufficient Optimality Conditions and Higher Order Exponential Type Generalized Invexities

First, a class of comprehensive higher order exponential type generalized B-(b, ρ, η, ω, θ, p̃, r̃, s̃)-invexities is introduced, which encompasses most of the existing generalized invexity concepts in the literature, including the Antczak type first order B-(b, η, p̃, r̃)-invexities as well as the Zalmai type (α, β, γ, η, ρ, θ)-invexities, and then a wide range of parametrically sufficient optimality conditions leading to the solvability for discrete minimax fractional programming problems are established with some other related results. To the best of our knowledge, the obtained results are new and general in nature relating the investigations on generalized higher order exponential type invexities.