Numerical solving of some optimization problems for semilinear elliptic equations

The project of research is optimal controlling problems for semilinear elliptic equations with controls in coefficients. The controls correspond to different controlling influences. Local and integral restrictions for controls are considered. Stable algorithms for the numerical solving are constructed. Constructed algorithms are based on the "Method of gradient projection", "Method of conditional gradient" and "Method of conjugate gradient projection". For the numerical solving the explicit formula for the grid functional gradient is obtained. In order to find the gradient of the grid functional under the fixed control the solutions of the difference scheme and the auxiliary dual problem are used