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.