A Generalization of Mixed Problems with an Application to Multiobjective Optimal Control

This paper generalizes to multiobjective optimization the notion of mixed problems as Philippe Michel calls it for single-objective optimization. This notion is then applied to a multiobjective control problem under constraints in the discrete time framework to obtain strong Pontryagin maximum principles in the finite-horizon case. The infinite-horizon case is also treated with conditions ensuring that the multipliers associated to the objective functions are not all zero.