Adjoint extremal problem for non-smooth functionals

The so-called adjoint extremal problem of searching for the optimal direction of a transition through a local extremum point is posed and studied. To this end, the concepts of local asymmetry and local excess of the functional at the extremum point are introduced, the minimization of which is the goal of the investigation. A number of examples for variational functionals with nonsmooth integrands of various types is considered.