Structural discontinuities to approximate some optimization problems with a nonmonotone impulsive character

Along the line of some of their previous works, the authors extend the treatment of a generic Bolza optimization problem for Lagrangian mechanical systems to the case where its impulsive character fails to be monotone. In the general situation being considered, many extended notions are properly used to obtain an adequate version of Pontryagin’s maximum principle and an existence theorem for the new well-posed extension of the original problem. Some more refined properties of the weak lower limit of the cost functional are also studied. Thus a necessary and sufficient condition for the contextual approximation theory to be satisfactory is practically established.