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$\epsilon$-optimality and duality for multiobjective fractional programming. (English) Zbl 0937.90097
Summary: Using the scalar $\epsilon$-parametric approach, we establish the Karush-Kuhn-Tucker (which we call KKT) necessary and sufficient conditions for an $\epsilon$-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 $\epsilon$-Pareto optimality of multiobjective fractional programming.
##### MSC:
 90C29 Multi-objective programming; goal programming 90C32 Fractional programming