On Minimax Fractional Semi-Infinite Programming Problems with Applications

Using some advanced tools of variational analysis and generalized differentiation, we establish necessary conditions for locally optimal solutions of minimax fractional programming problems under the limiting constraint qualification (LCQ). Sufficient conditions for such solutions to the considered problem are also provided by introducing generalized convex functions defined in terms of the limiting subdifferential for locally Lipschitz functions. In addition, some duality results for minimax fractional programming problems are also provided. Finally, by using the obtained results, we derive necessary and sufficient conditions for weak Pareto solutions to the multiobjective semi-infinite fractional optimization problem.