Optimal control problem with state constraints

We deal with methods of parameter continuation in applied optimal control problem using the maximum principle and the direct method of descent in the space of controls. Universal method for solving boundary-value problem with fixed right end is suggested. The example of the problems of dynamic portfolio is presented. The problem was solved by reducing to a linear programming (LP) one by integrating system the explicit Euler method. When one asked prescribed accuracy of the calculations due to the fineness of the partition of the segment we obtained LP problem of large dimension. This raises two major problems: (1) optimal solution within a reasonable time; (2) incorrectness of the LP problem. To find the optimal solution we apply the method of continuation the parameter. We divide the interval of integration into a number of nested segments and use parallel calculations. © Copyright by the paper's authors.