Method of decomposition in the optimal control problem for semilinear Sobolev type models

Due to the large number of applications the question of numerical solution of optimal control problems becomes very important. In the case of nonlinear state equations the search for optimal control is significantly difficult. One approach to the solution of this problem is the decomposition method. This method allows to linearize the original equation and to transfer the whole phenomenon of nonlinearity to the functional that greatly simplifies the numerical scheme for finding of approximate solution an optimal control problem.