Sequential Pareto Subdifferential Multi-Composition Rule and Application to Multiobjective Minimax Location Problems

In the absence of any qualification condition, we provide a sequential formula for the weak/proper Pareto subdifferential of multi-composed convex vector mappings. For illustrating this formula, we propose deriving sequential optimality conditions characterizing weakly/properly efficient solutions of multiobjective minimax location problems with infimal distances. We present an example of multiobjective bilevel programming problems with an extremal value function, where the standard Lagrange multipliers conditions can not be derived due to the lack of constraint qualification and the sequential conditions hold.