Optimality for nonsmooth minimax fractional and multiobjective fractional optimization

We establish optimality conditions for nonsmooth minimax fractional optimization problems with inequality and equality constraints in an Asplund space setting.Employing some advanced tools of variational analysis and generalized differentiation, we present necessary conditions for local optimal solutions under the constraint qualification.Sufficient conditions for the existence of global optimal solutions to the considered problem are also obtained by means of proposing the use of generalized convexaffine functions.In addition, some of these results are applied to multiobjective fractional optimization problems.Examples are given for analyzing and illustrating the obtained results.