ИСТИНА

This class of problems in finite-dimensional optimization has attracted attention with the advent of interior point-type methods. These methods have estimates of convergence in functional to the solution of a linear programming problem of polynomial type, which is much better than estimates of exponential type, which were known for the simplex method. The result aroused great interest and led to the improvement of similar estimates for the simplex method. This interest covered, in particular, optimal control problems and their various discretizations. This article considers linear optimal control problems with a boundary value linear programming problem at the right end of the time interval. A method for solving these problems is proposed. We prove the strong convergence of the method to the solution in all variables of the problem, except for the control, where the convergence is weak. The obtained result is based on sufficient optimality conditions. Instead of the maximum principle, the saddle point principle is used, which makes it possible to reliably obtain evidence-based solutions to the source problem.