In this contribution, the relationship between saddle points of Lagrangian functions associated with the inequality constrained multiobjective optimization problem and Fritz John critical points are presented under generalized notions of convexity. Assuming invexity and an extended Slater-type condition upon the multiobjective problem, a regular solution to the Fritz-John system is obtained that encompasses all the objective functions. Also, a new class of generalized convex problems is defined, and its connections with other existing classes are established.534917933