Optimal control problem with nonregular mixed constraints via penalty functions

Below we deduce necessary conditions of optimality for problems with nonregular mixed constraints (see Dmitruk(2009), Dmitruk and Osmolovskii(2022)) using the method of penalty functions similar to the one we previously used to solve optimization problems for control sweeping processes (see, e.g., de Pinho et al. (2022)), with pure state constraints de Pinho et al.,2024 and with regular mixed constraints (de Pinho et al.,2024). We intentionally consider a global minimum and the simplest boundary conditions.