1. On the Explicit Scheme with Variable Time Steps for Solving the Parabolic Optimal Control Problem
- Author
-
A. D. Romanenko
- Subjects
Pointwise ,Mathematical optimization ,Iterative method ,General Mathematics ,lcsh:Mathematics ,05 social sciences ,constraint on control ,Grid ,Optimal control ,lcsh:QA1-939 ,01 natural sciences ,Control function ,Domain (mathematical analysis) ,010101 applied mathematics ,Moment (mathematics) ,optimal control ,iterative method ,0502 economics and business ,050211 marketing ,variable step ,Uniqueness ,0101 mathematics ,Mathematics - Abstract
The paper deals with the optimal control problem, including the linear parabolic equation as a state problem. Pointwise constraints are imposed on the control function. The objective functional involves the observation function in the entire space-time domain. The optimal control problem is approximated by a finite dimensional problem with mesh approximation of the state equation by the explicit (forward Euler) mesh scheme with variable time steps. The existence of unique solutions for the continuous and mesh optimal control problems is proved. The Uzawa-type iterative method is used for solving the finite dimensional optimal control problem. The results of numerical experiments are presented.
- Published
- 2016