Jiménez, B.Novo, V.Huerga Pastor, Lidia2024-05-202024-05-202022-09-171573-2878http://doi.org/10.1007/s10957-022-02088-xhttps://hdl.handle.net/20.500.14468/12545In this paper, we introduce new notions of proper efficiency in the sense of Henig for a set optimization problem by using the set criterion of solution. The relationships between them are studied. Also, we compare these concepts with the homologous ones given by considering the vector criterion. Finally, a Lagrange multiplier rule for Henig proper solutions of a set optimization problem with a cone constraint is obtained under convexity hypotheses. Illustrative examples are also given.eninfo:eu-repo/semantics/openAccessjournal articleSet optimizationSet criterion of solutionVector criterion of solutionHenig proper efficiencyLagrange multipliers