The investigation proposed here has as its main objective the design, analysis, and testing of the so called projected Newton methods in computational optimization, with a special emphasis on the application of these methods to optimal control problems. Two kinds of problems are considered: disrete-time dynamical optimization problems and continuous time problems. It seems likely that the results of this research may be also applicable to other large-scale structured nonlinear optimization problems. The projected Newton method algorithms converge more rapidly than the standard first order, i.e. gradient based methods, yet the associated per iteration computational costs are still only proportional to n, where n is the number of subintervals of the time interval under consideration. A sizeable portion of the per iteration work can be organized for parallel computation. This research belongs to computational methods in optimization and control. Problems of this type arise in many applications, typically in optimization of trajectories for space vehicles and in calculations of optimal programs for control computers for various industrial processes.
