  In this paper, we consider a special class of nonlinear optimal control
problems, where the control variables are box-constrained and the objective
functional is strongly convex corresponding to control variables and separable
with respect to the state variables and control variables. We convert solving
the original nonlinear problem into solving a sequence of constrained
linear-quadratic optimal control problems by quasilinearization method. In
order to solve each linear-quadratic problem efficiently we turn to study its
dual problem. We formulate dual problem by the scheme of Fenchel duality, the
strong duality property and the saddle point property corresponding to primal
and dual problem are also proved, which together ensure that solving dual
problem is effective. Thus solving the sequence of control constrained
linear-quadratic optimal control problems obtained by quasilinearization
technique is substituted by solving the sequence of their dual problem. We
solve the sequence of dual problem and obtain the solution to primal control
constrained linear-quadratic problem by the saddle point property. Furthermore,
the fact that solution to each subproblem finally converges to the solution to
the optimality conditions of original nonlinear problem is also proved. After
that we carry out numerical experiments using present approach, for each
subproblem we formulate the discretized primal and dual problem by Euler
discretization scheme in our experiments. Efficiency of the present method is
validated by numerical results.
