Second order Φ,ρ-V-invexity and duality for semi-infinite minimax fractional programming

Semi-infinite minimax fractional programming problems with twice differentiable functions are considered. The second order parametric dual models are constructed for such optimization problems. Hence, several second order duality results are proved under assumptions that the functions constituting the considered semi-infinite minimax fractional programming problem and its duals are second order Φ,ρ-V-invex and/or second order generalized Φ,ρ-V-invex. Thus, a fairly large number of second order duality results established in the literarture is extended to a new class of nonconvex semi-infinite minimax fractional programming problems with twice differentiable functions.