A penalty/least-squares method for optimal control problems for first-order elliptic systems

摘要

A penalty/least-squares method for optimal control problems for first-order elliptic systems is considered wherein the constraint equations are enforced via penalization. The convergence, as the penalty parameter tends to zero, of the solution to the penalized optimal control problem to that of the unpenalized one is demonstrated as is the convergence of a gradient method for determining solutions of the penalized optimal control problem. Finally, finite element approximations of the penalized optimal control problem are studied and optimal error estimates are obtained.