An algorithm for optimal control problems with terminal equality constraints

We consider the problem P of minimizing g0(u) subject to the terminal equality constraint g(u)= 0. At any (possibly non-feasible) point u ?? L?? r[0,1], the alogorithm determines a search direction s(u) by solving a linearization of P at u, and a step length ??(u) by approximately minimizing an exact penalty function ??(u+??s(u), c) with respect to ?? using an Armijo type procedure. An automatic rule for c completes the specification of the algorithm, whose convergence is established.