On the explicit scheme with variable time steps for solving the parabolic optimal control problem

Abstract

The optimal control problem including a linear parabolic equation as the state problem is considered. Pointwise constraints are imposed on the control function. The objective functional contains a given observation function on the entire domain at each moment of time. The optimal control problem is approximated by a finite-dimensional problem with grid approximation of the state equation by using an explicit scheme with variable time steps. The existence and uniqueness of solutions for the continuous and grid optimal control problems are proved. The finite-dimensional optimal control problemis solved by the Udzawa iterationmethod. Results of numerical experiments are presented.