ON MODIFIED METHOD OF MULTISTEP COORDINATE DESCENT FOR OPTIMAL CONTROL PROBLEM FOR SEMILINEAR SOBOLEV-TYPE MODEL

Abstract

The paper describes a numerical method for solving the optimal control problem for a semilinear model of Sobolev-type. The method is based on both the modified projection Galerkin  method and the method of multistep coordinate  descent with memory. New numerical methods for solving nonlinear optimal control problems are need, because there exists a large number of applications  and it is difficult to find their analytical solutions. We consider mathematical model of regulating potential distribution of speed of the   filtered liquid free surface motion. In order to numerically investigate the mathematical model, we use  the sufficient conditions for the existence of an optimal control by solutions of Showalter-Sidorov problem for semilinear Sobolev type equation with $ s $-monotone and $ p $-coercive operator. We present the results of computational experiment that demonstrate the work of the proposed numerical method.