A numerical method for multistep optimization problems with stepwise computation of search direction

Non-linear problems of discrete optimal control with mixed constraints are considered. A mode of variation of the admissible control is proposed with the special property that the quantities determining it are chosen independently at different steps of the process. Necessary conditions for optimality are proved. An optimization algorithm, pertaining to the method of feasible directions, is developed and its convergence is proved. Results of numerical experiments are presented.