Parametric characterization of approximate quasi solutions in the class of quasidifferentiable multiobjective fractional programming problems

In this paper, the class of quasidifferentiable multiobjective fractional programming problems is investigated. The aim of this work is to study optimality conditions for approximate solutions of quasidifferentiable multiobjective fractional programming problems. Thus, using Dinkelbach approach, we prove the parametric Karush-Kuhn-Tucker-type necessary optimality conditions under the Kuntz-Scholtes constraint qualification for a feasible solution in the aforesaid nonsmooth vector optimization problem to be its approximate quasi weakly efficient solution. The sufficient conditions for approximate quasi (weakly) efficiency are also proved under assumptions that the functions involved are quasidifferentiable convex and/or quasidifferentiable generalized convex. Further, for the considered quasidifferentiable multiobjective fractional programming problem, its quasidifferentiable vector parametric dual problem in the sense of Schaible was formulated, and duality results are proved for these two nonsmooth vector optimization problems, also under quasidifferentiable convexity and/or quasidifferentiable generalized convexity hypotheses.