Mixed Lagrange function in minimax fractional programming problems

Abstract

In this paper, the aim of this work to study mixed Lagrange function for the minimax fractional programming problem with nonsmooth exponential (p, r) -invex functions with respect to η . We introduced a new concept of saddle point for a mixed Lagrange function. We present the equivalence between a saddle point of the mixed Lagrange function and an optimal solution in the considered minimax fractional programming problem under appropriate nonsmooth exponential (p, r) -invexity hypotheses.