Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

This talk is devoted to the Bolza optimal control problem under state constraints. We shall discuss necessary optimality conditions and provide some geometric conditions guaranteeing their normality. We also show how they can be applied to investigate regularity of optimal trajectories and of adjoint variables, as well as existence of optimal solutions to problems with Lagrangians not satisfying the Tonelli growth condition.