... multipliers, saddle points, and duality in vector optimization ofset-valued maps,” Journal of Mathematical Analysis and Applications, vol. 215, no. 2, pp. 297–316, 1997.15 W. Song, “Lagrangian duality ... “Proper efficiency and the theory of vector maximization,” Journal of MathematicalAnalysis and Applications, vol. 22, pp. 618–630, 1968.22 Journal of Inequalities and Applicationshence ϕTz ... proper saddle point of an appropriateset-valued Lagrange map, and obtained its necessary and sufficient optimality conditions.Simultaneously, we hav e also given some examples to illustrate these...