Semi-infinite minimax fractional programming under (Φ, <i>ρ</i>)-<i>V</i>-invexity and generalised (Φ, <i>ρ</i>)-<i>V</i>-invexity. Optimality

Abstract

Semi–infinite minimax fractional programming problems with both inequality and equality constraints are considered. The sets of parametric sufficient optimality conditions for a new class of non–convex differentiable semi–infinite minimax fractional programming problems are obtained under (generalised) (Φ, ρ)–V–invexity assumptions imposed on the objective and constraint functions. With the reference to the said functions, we extend some results of optimality for a larger class of non–convex semi–infinite minimax fractional programming problems in comparison to those ones, previously established in the literature under other generalised convex notions.