ϵ-Optimality and duality for multiobjective fractional programming

Using the scalar ϵ-parametric approach, we establish the Karush–Kuhn–Tucker (KKT) necessary and sufficient conditions for an ϵ-Pareto optimum of nondifferentiable multiobjective fractional objective functions subject to nondifferentiable convex inequality constraints, linear equality constraints, and abstract constraints. These optimality criteria are utilized as a basis for constructing one duality model with appropriate duality theorems. Subsequently, we employ scalar exact penalty function to transform the multiobjective fractional programming problem to an unconstrained problem. Under this case, we derive the KKT necessary and sufficient conditions without a constraint qualification for ϵ-Pareto optimality of multiobjective fractional programming.