Preconditioned Uzawa-type method for a state constrained parabolic optimal control problem with boundary control

Abstract

Iterative solution method for mesh approximation of an optimal control problem of a system governed by a linear parabolic equation is constructed and investigated. Control functions of the problem are in the right-hand side of the equation and in Neumann boundary condition, observation is in a part of the domain. Constraints on the control functions, state function and its time derivative are imposed. A mesh saddle point problem is constructed and preconditioned Uzawa-type method is applied to its solution. The main advantage of the iterative method is its effective implementation: every iteration step consists of the pointwise projections onto the segments and solving the linear mesh parabolic equations.