  A class of exact penalty-type local search methods for optimal control
problems with nonsmooth cost functional, nonsmooth (but continuous) dynamics,
and nonsmooth state and control constraints is presented, in which the the
penalty parameter and several line search parameters are adaptively adjusted
during the optimisation process. This class of methods is applicable to
problems having a known DC (Difference-of-Convex functions) structure and in
its core is based on the classical DCA method, combined with the steering exact
penalty rules for updating the penalty parameter and an adaptive nonmonotone
line search procedure. Under the assumption that all auxiliary subproblems are
solved only approximately (that is, with finite precision), we prove the
correctness of the proposed family of methods and present its detailed
convergence analysis. The performance of several different versions of the
method is illustrated by means of a numerical example, in which the methods are
applied to a semi-academic optimal control problem with a nonsmooth nonconvex
state constraint.
