文摘
In this work we introduce two approximate duality approaches for vector optimization problems. The first one by means of approximate solutions of a scalar Lagrangian, and the second one by considering \((C,\varepsilon )\)-proper efficient solutions of a recently introduced set-valued vector Lagrangian. In both approaches we obtain weak and strong duality results for \((C,\varepsilon )\)-proper efficient solutions of the primal problem, under generalized convexity assumptions. Due to the suitable limit behaviour of the \((C,\varepsilon )\)-proper efficient solutions when the error \(\varepsilon \) tends to zero, the obtained duality results extend and improve several others in the literature.