Local search for nonconvex optimal control problems of Bolza

A nonconvex optimal control problem whose nonconvexity is generated by an integro-terminal objective functional is considered. A new local search method that allows obtaining a control process $(x_*(\cdot), u_*(\cdot))$ satisfying, in particular, Pontryagin's maximum principle is proposed. Some peculiar properties of convergence of the algorithm are studied. Furthermore, some preliminary numerical simulations have been conducted the results of which certify a rather competitive efficiency of the algorithm.